Autoregressive Moving Average (ARMA): Sunspots data
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.. _tsa_arma_0_notebook:

`Link to Notebook GitHub <https://github.com/statsmodels/statsmodels/blob/master/examples/notebooks/tsa_arma_0.ipynb>`_

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   <div class="highlight"><pre><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
   <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
   <span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span>
   <span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
   <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
   
   <span class="kn">import</span> <span class="nn">statsmodels.api</span> <span class="kn">as</span> <span class="nn">sm</span>
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   <div class="highlight"><pre><span class="kn">from</span> <span class="nn">statsmodels.graphics.api</span> <span class="kn">import</span> <span class="n">qqplot</span>
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   <h2 id="Sunpots-Data">Sunpots Data<a class="anchor-link" href="#Sunpots-Data">&#182;</a></h2>
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   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">sunspots</span><span class="o">.</span><span class="n">NOTE</span><span class="p">)</span>
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   ::
   
       Number of Observations - 309 (Annual 1700 - 2008)
       Number of Variables - 1
       Variable name definitions::
   
           SUNACTIVITY - Number of sunspots for each year
   
       The data file contains a &apos;YEAR&apos; variable that is not returned by load.
   
   
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   <div class="highlight"><pre><span class="n">dta</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">sunspots</span><span class="o">.</span><span class="n">load_pandas</span><span class="p">()</span><span class="o">.</span><span class="n">data</span>
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   <div class="highlight"><pre><span class="n">dta</span><span class="o">.</span><span class="n">index</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Index</span><span class="p">(</span><span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">datetools</span><span class="o">.</span><span class="n">dates_from_range</span><span class="p">(</span><span class="s1">&#39;1700&#39;</span><span class="p">,</span> <span class="s1">&#39;2008&#39;</span><span class="p">))</span>
   <span class="k">del</span> <span class="n">dta</span><span class="p">[</span><span class="s2">&quot;YEAR&quot;</span><span class="p">]</span>
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   <div class="highlight"><pre><span class="n">dta</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">));</span>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
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   &lt;matplotlib.figure.Figure at 0x7fb773c5af50&gt;
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   <div class="prompt input_prompt">In&nbsp;[7]:</div>
   <div class="inner_cell">
       <div class="input_area">
   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax1</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">211</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_acf</span><span class="p">(</span><span class="n">dta</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">)</span>
   <span class="n">ax2</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_pacf</span><span class="p">(</span><span class="n">dta</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax2</span><span class="p">)</span>
   </pre></div>
   
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
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   &lt;matplotlib.figure.Figure at 0x7fb773c6a810&gt;
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   <div class="prompt input_prompt">In&nbsp;[8]:</div>
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   <div class="highlight"><pre><span class="n">arma_mod20</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">ARMA</span><span class="p">(</span><span class="n">dta</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
   <span class="k">print</span><span class="p">(</span><span class="n">arma_mod20</span><span class="o">.</span><span class="n">params</span><span class="p">)</span>
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   const                49.659366
   ar.L1.SUNACTIVITY     1.390656
   ar.L2.SUNACTIVITY    -0.688571
   dtype: float64
   
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   <div class="highlight"><pre><span class="n">arma_mod30</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">ARMA</span><span class="p">(</span><span class="n">dta</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
   </pre></div>
   
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   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">arma_mod20</span><span class="o">.</span><span class="n">aic</span><span class="p">,</span> <span class="n">arma_mod20</span><span class="o">.</span><span class="n">bic</span><span class="p">,</span> <span class="n">arma_mod20</span><span class="o">.</span><span class="n">hqic</span><span class="p">)</span>
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   2622.63633806 2637.56970317 2628.60672591
   
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   <div class="prompt input_prompt">In&nbsp;[11]:</div>
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   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">arma_mod30</span><span class="o">.</span><span class="n">params</span><span class="p">)</span>
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   const                49.749796
   ar.L1.SUNACTIVITY     1.300810
   ar.L2.SUNACTIVITY    -0.508093
   ar.L3.SUNACTIVITY    -0.129650
   dtype: float64
   
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   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">arma_mod30</span><span class="o">.</span><span class="n">aic</span><span class="p">,</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">bic</span><span class="p">,</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">hqic</span><span class="p">)</span>
   </pre></div>
   
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   2619.4036287 2638.07033508 2626.86661351
   
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   <ul>
   <li>Does our model obey the theory?</li>
   </ul>
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   <div class="prompt input_prompt">In&nbsp;[13]:</div>
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       <div class="input_area">
   <div class="highlight"><pre><span class="n">sm</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">durbin_watson</span><span class="p">(</span><span class="n">arma_mod30</span><span class="o">.</span><span class="n">resid</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
   </pre></div>
   
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   1.9564806905406757
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   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">resid</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">);</span>
   </pre></div>
   
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
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   &lt;matplotlib.figure.Figure at 0x7fb77827ba10&gt;
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   <div class="highlight"><pre><span class="n">resid</span> <span class="o">=</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">resid</span>
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   <div class="highlight"><pre><span class="n">stats</span><span class="o">.</span><span class="n">normaltest</span><span class="p">(</span><span class="n">resid</span><span class="p">)</span>
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   NormaltestResult(statistic=49.845037117754686, pvalue=1.5006786874160669e-11)
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   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">qqplot</span><span class="p">(</span><span class="n">resid</span><span class="p">,</span> <span class="n">line</span><span class="o">=</span><span class="s1">&#39;q&#39;</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">fit</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
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   &lt;matplotlib.figure.Figure at 0x7fb773ad7c50&gt;
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   <div class="prompt input_prompt">In&nbsp;[18]:</div>
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       <div class="input_area">
   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax1</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">211</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_acf</span><span class="p">(</span><span class="n">resid</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">)</span>
   <span class="n">ax2</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_pacf</span><span class="p">(</span><span class="n">resid</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax2</span><span class="p">)</span>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
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   &lt;matplotlib.figure.Figure at 0x7fb773993f90&gt;
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   <div class="cell border-box-sizing code_cell rendered">
   <div class="input">
   <div class="prompt input_prompt">In&nbsp;[19]:</div>
   <div class="inner_cell">
       <div class="input_area">
   <div class="highlight"><pre><span class="n">r</span><span class="p">,</span><span class="n">q</span><span class="p">,</span><span class="n">p</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">acf</span><span class="p">(</span><span class="n">resid</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">qstat</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
   <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">41</span><span class="p">),</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">q</span><span class="p">,</span> <span class="n">p</span><span class="p">]</span>
   <span class="n">table</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;lag&#39;</span><span class="p">,</span> <span class="s2">&quot;AC&quot;</span><span class="p">,</span> <span class="s2">&quot;Q&quot;</span><span class="p">,</span> <span class="s2">&quot;Prob(&gt;Q)&quot;</span><span class="p">])</span>
   <span class="k">print</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s1">&#39;lag&#39;</span><span class="p">))</span>
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              AC          Q      Prob(&gt;Q)
   lag                                   
   1    0.009179   0.026287  8.712008e-01
   2    0.041793   0.573048  7.508690e-01
   3   -0.001334   0.573607  9.024469e-01
   4    0.136089   6.408955  1.706181e-01
   5    0.092469   9.111881  1.046840e-01
   6    0.091949  11.793308  6.674192e-02
   7    0.068748  13.297273  6.518822e-02
   8   -0.015020  13.369300  9.975911e-02
   9    0.187592  24.641988  3.393810e-03
   10   0.213718  39.322079  2.229398e-05
   11   0.201082  52.361229  2.344860e-07
   12   0.117182  56.804288  8.573905e-08
   13  -0.014055  56.868423  1.893827e-07
   14   0.015398  56.945664  3.997499e-07
   15  -0.024967  57.149416  7.741175e-07
   16   0.080916  59.296873  6.871888e-07
   17   0.041138  59.853844  1.110899e-06
   18  -0.052021  60.747533  1.548371e-06
   19   0.062496  62.041796  1.831572e-06
   20  -0.010301  62.077084  3.381114e-06
   21   0.074453  63.926758  3.193467e-06
   22   0.124955  69.154873  8.978021e-07
   23   0.093162  72.071136  5.799571e-07
   24  -0.082152  74.346787  4.712847e-07
   25   0.015695  74.430143  8.288748e-07
   26  -0.025037  74.643000  1.367237e-06
   27  -0.125861  80.041239  3.722446e-07
   28   0.053225  81.010073  4.716129e-07
   29  -0.038693  81.523899  6.916415e-07
   30  -0.016904  81.622318  1.151625e-06
   31  -0.019296  81.751031  1.868708e-06
   32   0.104990  85.575151  8.927700e-07
   33   0.040086  86.134651  1.247474e-06
   34   0.008829  86.161894  2.047769e-06
   35   0.014588  86.236531  3.263719e-06
   36  -0.119329  91.248977  1.084426e-06
   37  -0.036665  91.723945  1.521884e-06
   38  -0.046193  92.480592  1.938687e-06
   39  -0.017768  92.592961  2.990607e-06
   40  -0.006220  92.606784  4.696872e-06
   
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   <ul>
   <li>This indicates a lack of fit.</li>
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   <li>In-sample dynamic prediction. How good does our model do?</li>
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   <div class="highlight"><pre><span class="n">predict_sunspots</span> <span class="o">=</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="s1">&#39;1990&#39;</span><span class="p">,</span> <span class="s1">&#39;2012&#39;</span><span class="p">,</span> <span class="n">dynamic</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
   <span class="k">print</span><span class="p">(</span><span class="n">predict_sunspots</span><span class="p">)</span>
   </pre></div>
   
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   1990-12-31    167.047353
   1991-12-31    140.992848
   1992-12-31     94.858876
   1993-12-31     46.860614
   1994-12-31     11.242300
   1995-12-31     -4.721532
   1996-12-31     -1.167078
   1997-12-31     16.185598
   1998-12-31     39.021839
   1999-12-31     59.449843
   2000-12-31     72.170093
   2001-12-31     75.376689
   2002-12-31     70.436311
   2003-12-31     60.731396
   2004-12-31     50.201584
   2005-12-31     42.075817
   2006-12-31     38.114099
   2007-12-31     38.454487
   2008-12-31     41.963690
   2009-12-31     46.869181
   2010-12-31     51.423160
   2011-12-31     54.399610
   2012-12-31     55.321566
   Freq: A-DEC, dtype: float64
   
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   <div class="highlight"><pre><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">dta</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="s1">&#39;1950&#39;</span><span class="p">:]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">arma_mod30</span><span class="o">.</span><span class="n">plot_predict</span><span class="p">(</span><span class="s1">&#39;1990&#39;</span><span class="p">,</span> <span class="s1">&#39;2012&#39;</span><span class="p">,</span> <span class="n">dynamic</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">plot_insample</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
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   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
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   &lt;matplotlib.figure.Figure at 0x7fb7737c7c10&gt;
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   <div class="highlight"><pre><span class="k">def</span> <span class="nf">mean_forecast_err</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">yhat</span><span class="p">):</span>
       <span class="k">return</span> <span class="n">y</span><span class="o">.</span><span class="n">sub</span><span class="p">(</span><span class="n">yhat</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
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   <div class="highlight"><pre><span class="n">mean_forecast_err</span><span class="p">(</span><span class="n">dta</span><span class="o">.</span><span class="n">SUNACTIVITY</span><span class="p">,</span> <span class="n">predict_sunspots</span><span class="p">)</span>
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   5.6371143703450644
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   <h3 id="Exercise:-Can-you-obtain-a-better-fit-for-the-Sunspots-model?-(Hint:-sm.tsa.AR-has-a-method-select_order)">Exercise: Can you obtain a better fit for the Sunspots model? (Hint: sm.tsa.AR has a method select_order)<a class="anchor-link" href="#Exercise:-Can-you-obtain-a-better-fit-for-the-Sunspots-model?-(Hint:-sm.tsa.AR-has-a-method-select_order)">&#182;</a></h3>
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   <h3 id="Simulated-ARMA(4,1):-Model-Identification-is-Difficult">Simulated ARMA(4,1): Model Identification is Difficult<a class="anchor-link" href="#Simulated-ARMA(4,1):-Model-Identification-is-Difficult">&#182;</a></h3>
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   <div class="highlight"><pre><span class="kn">from</span> <span class="nn">statsmodels.tsa.arima_process</span> <span class="kn">import</span> <span class="n">arma_generate_sample</span><span class="p">,</span> <span class="n">ArmaProcess</span>
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   <div class="highlight"><pre><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">1234</span><span class="p">)</span>
   <span class="c1"># include zero-th lag</span>
   <span class="n">arparams</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">75</span><span class="p">,</span> <span class="o">-.</span><span class="mi">65</span><span class="p">,</span> <span class="o">-.</span><span class="mi">55</span><span class="p">,</span> <span class="o">.</span><span class="mi">9</span><span class="p">])</span>
   <span class="n">maparams</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">65</span><span class="p">])</span>
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   <p>Let&#39;s make sure this model is estimable.</p>
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   <div class="highlight"><pre><span class="n">arma_t</span> <span class="o">=</span> <span class="n">ArmaProcess</span><span class="p">(</span><span class="n">arparams</span><span class="p">,</span> <span class="n">maparams</span><span class="p">)</span>
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   <div class="highlight"><pre><span class="n">arma_t</span><span class="o">.</span><span class="n">isinvertible</span><span class="p">()</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">TypeError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-251-d3a1a0e5898b&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>arma_t<span class="ansiblue">.</span>isinvertible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">TypeError</span>: &apos;bool&apos; object is not callable</pre>
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   <div class="highlight"><pre><span class="n">arma_t</span><span class="o">.</span><span class="n">isstationary</span><span class="p">()</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">TypeError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-252-55a9b2cc43b1&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>arma_t<span class="ansiblue">.</span>isstationary<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">TypeError</span>: &apos;bool&apos; object is not callable</pre>
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   <li>What does this mean?</li>
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   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
   <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">arma_t</span><span class="o">.</span><span class="n">generate_sample</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="mi">50</span><span class="p">));</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
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   <span class="ansigreen">&lt;ipython-input-253-d059f8971c1a&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">      1</span> fig <span class="ansiblue">=</span> plt<span class="ansiblue">.</span>figure<span class="ansiblue">(</span>figsize<span class="ansiblue">=</span><span class="ansiblue">(</span><span class="ansicyan">12</span><span class="ansiblue">,</span><span class="ansicyan">8</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      2</span> ax <span class="ansiblue">=</span> fig<span class="ansiblue">.</span>add_subplot<span class="ansiblue">(</span><span class="ansicyan">111</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">----&gt; 3</span><span class="ansired"> </span>ax<span class="ansiblue">.</span>plot<span class="ansiblue">(</span>arma_t<span class="ansiblue">.</span>generate_sample<span class="ansiblue">(</span>size<span class="ansiblue">=</span><span class="ansicyan">50</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">;</span><span class="ansiblue"></span>
   
   <span class="ansired">TypeError</span>: generate_sample() got an unexpected keyword argument &apos;size&apos;</pre>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
   </pre>
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   &lt;matplotlib.figure.Figure at 0x7fb77397d3d0&gt;
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   <div class="highlight"><pre><span class="n">arparams</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">35</span><span class="p">,</span> <span class="o">-.</span><span class="mi">15</span><span class="p">,</span> <span class="o">.</span><span class="mi">55</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">])</span>
   <span class="n">maparams</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">65</span><span class="p">])</span>
   <span class="n">arma_t</span> <span class="o">=</span> <span class="n">ArmaProcess</span><span class="p">(</span><span class="n">arparams</span><span class="p">,</span> <span class="n">maparams</span><span class="p">)</span>
   <span class="n">arma_t</span><span class="o">.</span><span class="n">isstationary</span><span class="p">()</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">TypeError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-254-317f1b2ac56b&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">      2</span> maparams <span class="ansiblue">=</span> np<span class="ansiblue">.</span>array<span class="ansiblue">(</span><span class="ansiblue">[</span><span class="ansicyan">1</span><span class="ansiblue">,</span> <span class="ansicyan">.65</span><span class="ansiblue">]</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      3</span> arma_t <span class="ansiblue">=</span> ArmaProcess<span class="ansiblue">(</span>arparams<span class="ansiblue">,</span> maparams<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">----&gt; 4</span><span class="ansired"> </span>arma_t<span class="ansiblue">.</span>isstationary<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">TypeError</span>: &apos;bool&apos; object is not callable</pre>
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   <div class="highlight"><pre><span class="n">arma_rvs</span> <span class="o">=</span> <span class="n">arma_t</span><span class="o">.</span><span class="n">generate_sample</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">burnin</span><span class="o">=</span><span class="mi">250</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">2.5</span><span class="p">)</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">TypeError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-255-e0a3cc13cb6e&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>arma_rvs <span class="ansiblue">=</span> arma_t<span class="ansiblue">.</span>generate_sample<span class="ansiblue">(</span>size<span class="ansiblue">=</span><span class="ansicyan">500</span><span class="ansiblue">,</span> burnin<span class="ansiblue">=</span><span class="ansicyan">250</span><span class="ansiblue">,</span> scale<span class="ansiblue">=</span><span class="ansicyan">2.5</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">TypeError</span>: generate_sample() got an unexpected keyword argument &apos;size&apos;</pre>
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   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax1</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">211</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_acf</span><span class="p">(</span><span class="n">arma_rvs</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">)</span>
   <span class="n">ax2</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">graphics</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">plot_pacf</span><span class="p">(</span><span class="n">arma_rvs</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax2</span><span class="p">)</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">NameError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-256-8e761b44cfae&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">      1</span> fig <span class="ansiblue">=</span> plt<span class="ansiblue">.</span>figure<span class="ansiblue">(</span>figsize<span class="ansiblue">=</span><span class="ansiblue">(</span><span class="ansicyan">12</span><span class="ansiblue">,</span><span class="ansicyan">8</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      2</span> ax1 <span class="ansiblue">=</span> fig<span class="ansiblue">.</span>add_subplot<span class="ansiblue">(</span><span class="ansicyan">211</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">----&gt; 3</span><span class="ansired"> </span>fig <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>graphics<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>plot_acf<span class="ansiblue">(</span>arma_rvs<span class="ansiblue">,</span> lags<span class="ansiblue">=</span><span class="ansicyan">40</span><span class="ansiblue">,</span> ax<span class="ansiblue">=</span>ax1<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      4</span> ax2 <span class="ansiblue">=</span> fig<span class="ansiblue">.</span>add_subplot<span class="ansiblue">(</span><span class="ansicyan">212</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      5</span> fig <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>graphics<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>plot_pacf<span class="ansiblue">(</span>arma_rvs<span class="ansiblue">,</span> lags<span class="ansiblue">=</span><span class="ansicyan">40</span><span class="ansiblue">,</span> ax<span class="ansiblue">=</span>ax2<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">NameError</span>: name &apos;arma_rvs&apos; is not defined</pre>
   </div>
   </div>
   
   <div class="output_area"><div class="prompt"></div>
   <div class="output_subarea output_stream output_stdout output_text">
   <pre>
   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
   </pre>
   </div>
   </div>
   
   <div class="output_area"><div class="prompt"></div>
   <div class="output_subarea output_text output_pyerr">
   <pre>
   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
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   &lt;matplotlib.figure.Figure at 0x7fb773a572d0&gt;
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   <ul>
   <li>For mixed ARMA processes the Autocorrelation function is a mixture of exponentials and damped sine waves after (q-p) lags. </li>
   <li>The partial autocorrelation function is a mixture of exponentials and dampened sine waves after (p-q) lags.</li>
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   <div class="highlight"><pre><span class="n">arma11</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">ARMA</span><span class="p">(</span><span class="n">arma_rvs</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
   <span class="n">resid</span> <span class="o">=</span> <span class="n">arma11</span><span class="o">.</span><span class="n">resid</span>
   <span class="n">r</span><span class="p">,</span><span class="n">q</span><span class="p">,</span><span class="n">p</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">acf</span><span class="p">(</span><span class="n">resid</span><span class="p">,</span> <span class="n">qstat</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
   <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">41</span><span class="p">),</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">q</span><span class="p">,</span> <span class="n">p</span><span class="p">]</span>
   <span class="n">table</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;lag&#39;</span><span class="p">,</span> <span class="s2">&quot;AC&quot;</span><span class="p">,</span> <span class="s2">&quot;Q&quot;</span><span class="p">,</span> <span class="s2">&quot;Prob(&gt;Q)&quot;</span><span class="p">])</span>
   <span class="k">print</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s1">&#39;lag&#39;</span><span class="p">))</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">NameError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-257-03653831c71c&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>arma11 <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>ARMA<span class="ansiblue">(</span>arma_rvs<span class="ansiblue">,</span> <span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">,</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">.</span>fit<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      2</span> resid <span class="ansiblue">=</span> arma11<span class="ansiblue">.</span>resid<span class="ansiblue"></span>
   <span class="ansigreen">      3</span> r<span class="ansiblue">,</span>q<span class="ansiblue">,</span>p <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>acf<span class="ansiblue">(</span>resid<span class="ansiblue">,</span> qstat<span class="ansiblue">=</span>True<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      4</span> data <span class="ansiblue">=</span> np<span class="ansiblue">.</span>c_<span class="ansiblue">[</span>range<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">,</span><span class="ansicyan">41</span><span class="ansiblue">)</span><span class="ansiblue">,</span> r<span class="ansiblue">[</span><span class="ansicyan">1</span><span class="ansiblue">:</span><span class="ansiblue">]</span><span class="ansiblue">,</span> q<span class="ansiblue">,</span> p<span class="ansiblue">]</span><span class="ansiblue"></span>
   <span class="ansigreen">      5</span> table <span class="ansiblue">=</span> pd<span class="ansiblue">.</span>DataFrame<span class="ansiblue">(</span>data<span class="ansiblue">,</span> columns<span class="ansiblue">=</span><span class="ansiblue">[</span><span class="ansiblue">&apos;lag&apos;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;AC&quot;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;Q&quot;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;Prob(&gt;Q)&quot;</span><span class="ansiblue">]</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">NameError</span>: name &apos;arma_rvs&apos; is not defined</pre>
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   <div class="highlight"><pre><span class="n">arma41</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">ARMA</span><span class="p">(</span><span class="n">arma_rvs</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
   <span class="n">resid</span> <span class="o">=</span> <span class="n">arma41</span><span class="o">.</span><span class="n">resid</span>
   <span class="n">r</span><span class="p">,</span><span class="n">q</span><span class="p">,</span><span class="n">p</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">acf</span><span class="p">(</span><span class="n">resid</span><span class="p">,</span> <span class="n">qstat</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
   <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">41</span><span class="p">),</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">q</span><span class="p">,</span> <span class="n">p</span><span class="p">]</span>
   <span class="n">table</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;lag&#39;</span><span class="p">,</span> <span class="s2">&quot;AC&quot;</span><span class="p">,</span> <span class="s2">&quot;Q&quot;</span><span class="p">,</span> <span class="s2">&quot;Prob(&gt;Q)&quot;</span><span class="p">])</span>
   <span class="k">print</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s1">&#39;lag&#39;</span><span class="p">))</span>
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">NameError</span>                                 Traceback (most recent call last)
   <span class="ansigreen">&lt;ipython-input-258-30d9c2f35894&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
   <span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>arma41 <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>ARMA<span class="ansiblue">(</span>arma_rvs<span class="ansiblue">,</span> <span class="ansiblue">(</span><span class="ansicyan">4</span><span class="ansiblue">,</span><span class="ansicyan">1</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue">.</span>fit<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      2</span> resid <span class="ansiblue">=</span> arma41<span class="ansiblue">.</span>resid<span class="ansiblue"></span>
   <span class="ansigreen">      3</span> r<span class="ansiblue">,</span>q<span class="ansiblue">,</span>p <span class="ansiblue">=</span> sm<span class="ansiblue">.</span>tsa<span class="ansiblue">.</span>acf<span class="ansiblue">(</span>resid<span class="ansiblue">,</span> qstat<span class="ansiblue">=</span>True<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">      4</span> data <span class="ansiblue">=</span> np<span class="ansiblue">.</span>c_<span class="ansiblue">[</span>range<span class="ansiblue">(</span><span class="ansicyan">1</span><span class="ansiblue">,</span><span class="ansicyan">41</span><span class="ansiblue">)</span><span class="ansiblue">,</span> r<span class="ansiblue">[</span><span class="ansicyan">1</span><span class="ansiblue">:</span><span class="ansiblue">]</span><span class="ansiblue">,</span> q<span class="ansiblue">,</span> p<span class="ansiblue">]</span><span class="ansiblue"></span>
   <span class="ansigreen">      5</span> table <span class="ansiblue">=</span> pd<span class="ansiblue">.</span>DataFrame<span class="ansiblue">(</span>data<span class="ansiblue">,</span> columns<span class="ansiblue">=</span><span class="ansiblue">[</span><span class="ansiblue">&apos;lag&apos;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;AC&quot;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;Q&quot;</span><span class="ansiblue">,</span> <span class="ansiblue">&quot;Prob(&gt;Q)&quot;</span><span class="ansiblue">]</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">NameError</span>: name &apos;arma_rvs&apos; is not defined</pre>
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   <h3 id="Exercise:-How-good-of-in-sample-prediction-can-you-do-for-another-series,-say,-CPI">Exercise: How good of in-sample prediction can you do for another series, say, CPI<a class="anchor-link" href="#Exercise:-How-good-of-in-sample-prediction-can-you-do-for-another-series,-say,-CPI">&#182;</a></h3>
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   <div class="highlight"><pre><span class="n">macrodta</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">macrodata</span><span class="o">.</span><span class="n">load_pandas</span><span class="p">()</span><span class="o">.</span><span class="n">data</span>
   <span class="n">macrodta</span><span class="o">.</span><span class="n">index</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Index</span><span class="p">(</span><span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">datetools</span><span class="o">.</span><span class="n">dates_from_range</span><span class="p">(</span><span class="s1">&#39;1959Q1&#39;</span><span class="p">,</span> <span class="s1">&#39;2009Q3&#39;</span><span class="p">))</span>
   <span class="n">cpi</span> <span class="o">=</span> <span class="n">macrodta</span><span class="p">[</span><span class="s2">&quot;cpi&quot;</span><span class="p">]</span>
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   <h4 id="Hint:">Hint:<a class="anchor-link" href="#Hint:">&#182;</a></h4>
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   <div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
   <span class="n">ax</span> <span class="o">=</span> <span class="n">cpi</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">);</span>
   <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span>
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   Error in callback &lt;function post_execute at 0x7fb786441500&gt; (for post_execute):
   
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   <span class="ansired">---------------------------------------------------------------------------</span>
   <span class="ansired">RuntimeError</span>                              Traceback (most recent call last)
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc</span> in <span class="ansicyan">post_execute</span><span class="ansiblue">()</span>
   <span class="ansigreen">    145</span>             <span class="ansigreen">def</span> post_execute<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    146</span>                 <span class="ansigreen">if</span> matplotlib<span class="ansiblue">.</span>is_interactive<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 147</span><span class="ansired">                     </span>draw_all<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    148</span> <span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansired"># IPython &gt;= 2</span><span class="ansiblue"></span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc</span> in <span class="ansicyan">draw_all</span><span class="ansiblue">(cls, force)</span>
   <span class="ansigreen">    148</span>         <span class="ansigreen">for</span> f_mgr <span class="ansigreen">in</span> cls<span class="ansiblue">.</span>get_all_fig_managers<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    149</span>             <span class="ansigreen">if</span> force <span class="ansigreen">or</span> f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>stale<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 150</span><span class="ansired">                 </span>f_mgr<span class="ansiblue">.</span>canvas<span class="ansiblue">.</span>draw_idle<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    151</span> <span class="ansiblue"></span>
   <span class="ansigreen">    152</span> atexit<span class="ansiblue">.</span>register<span class="ansiblue">(</span>Gcf<span class="ansiblue">.</span>destroy_all<span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc</span> in <span class="ansicyan">draw_idle</span><span class="ansiblue">(self, *args, **kwargs)</span>
   <span class="ansigreen">   2024</span>         <span class="ansigreen">if</span> <span class="ansigreen">not</span> self<span class="ansiblue">.</span>_is_idle_drawing<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   2025</span>             <span class="ansigreen">with</span> self<span class="ansiblue">.</span>_idle_draw_cntx<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2026</span><span class="ansired">                 </span>self<span class="ansiblue">.</span>draw<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2027</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2028</span>     <span class="ansigreen">def</span> draw_cursor<span class="ansiblue">(</span>self<span class="ansiblue">,</span> event<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self)</span>
   <span class="ansigreen">    472</span> <span class="ansiblue"></span>
   <span class="ansigreen">    473</span>         <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 474</span><span class="ansired">             </span>self<span class="ansiblue">.</span>figure<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>self<span class="ansiblue">.</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    475</span>         <span class="ansigreen">finally</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    476</span>             RendererAgg<span class="ansiblue">.</span>lock<span class="ansiblue">.</span>release<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/figure.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">   1157</span>         dsu<span class="ansiblue">.</span>sort<span class="ansiblue">(</span>key<span class="ansiblue">=</span>itemgetter<span class="ansiblue">(</span><span class="ansicyan">0</span><span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1158</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a<span class="ansiblue">,</span> func<span class="ansiblue">,</span> args <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1159</span><span class="ansired">             </span>func<span class="ansiblue">(</span><span class="ansiblue">*</span>args<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1160</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1161</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;figure&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, inframe)</span>
   <span class="ansigreen">   2322</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2323</span>         <span class="ansigreen">for</span> zorder<span class="ansiblue">,</span> a <span class="ansigreen">in</span> dsu<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 2324</span><span class="ansired">             </span>a<span class="ansiblue">.</span>draw<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   2325</span> <span class="ansiblue"></span>
   <span class="ansigreen">   2326</span>         renderer<span class="ansiblue">.</span>close_group<span class="ansiblue">(</span><span class="ansiblue">&apos;axes&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/artist.pyc</span> in <span class="ansicyan">draw_wrapper</span><span class="ansiblue">(artist, renderer, *args, **kwargs)</span>
   <span class="ansigreen">     59</span>     <span class="ansigreen">def</span> draw_wrapper<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">     60</span>         before<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">---&gt; 61</span><span class="ansired">         </span>draw<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">,</span> <span class="ansiblue">*</span>args<span class="ansiblue">,</span> <span class="ansiblue">**</span>kwargs<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     62</span>         after<span class="ansiblue">(</span>artist<span class="ansiblue">,</span> renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">     63</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">draw</span><span class="ansiblue">(self, renderer, *args, **kwargs)</span>
   <span class="ansigreen">   1106</span>         ticks_to_draw <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_update_ticks<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1107</span>         ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
   <span class="ansigreen">-&gt; 1108</span><span class="ansired">                                                                 renderer)
   </span><span class="ansigreen">   1109</span> <span class="ansiblue"></span>
   <span class="ansigreen">   1110</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks_to_draw<span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/axis.pyc</span> in <span class="ansicyan">_get_tick_bboxes</span><span class="ansiblue">(self, ticks, renderer)</span>
   <span class="ansigreen">   1056</span>         <span class="ansigreen">for</span> tick <span class="ansigreen">in</span> ticks<span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">   1057</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label1On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">-&gt; 1058</span><span class="ansired">                 </span>extent <span class="ansiblue">=</span> tick<span class="ansiblue">.</span>label1<span class="ansiblue">.</span>get_window_extent<span class="ansiblue">(</span>renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1059</span>                 ticklabelBoxes<span class="ansiblue">.</span>append<span class="ansiblue">(</span>extent<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">   1060</span>             <span class="ansigreen">if</span> tick<span class="ansiblue">.</span>label2On <span class="ansigreen">and</span> tick<span class="ansiblue">.</span>label2<span class="ansiblue">.</span>get_visible<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">get_window_extent</span><span class="ansiblue">(self, renderer, dpi)</span>
   <span class="ansigreen">    959</span>             <span class="ansigreen">raise</span> RuntimeError<span class="ansiblue">(</span><span class="ansiblue">&apos;Cannot get window extent w/o renderer&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    960</span> <span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 961</span><span class="ansired">         </span>bbox<span class="ansiblue">,</span> info<span class="ansiblue">,</span> descent <span class="ansiblue">=</span> self<span class="ansiblue">.</span>_get_layout<span class="ansiblue">(</span>self<span class="ansiblue">.</span>_renderer<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    962</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_unitless_position<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    963</span>         x<span class="ansiblue">,</span> y <span class="ansiblue">=</span> self<span class="ansiblue">.</span>get_transform<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue">.</span>transform_point<span class="ansiblue">(</span><span class="ansiblue">(</span>x<span class="ansiblue">,</span> y<span class="ansiblue">)</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/text.pyc</span> in <span class="ansicyan">_get_layout</span><span class="ansiblue">(self, renderer)</span>
   <span class="ansigreen">    350</span>         tmp, lp_h, lp_bl = renderer.get_text_width_height_descent(&apos;lp&apos;,
   <span class="ansigreen">    351</span>                                                          self<span class="ansiblue">.</span>_fontproperties<span class="ansiblue">,</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 352</span><span class="ansired">                                                          ismath=False)
   </span><span class="ansigreen">    353</span>         offsety <span class="ansiblue">=</span> <span class="ansiblue">(</span>lp_h <span class="ansiblue">-</span> lp_bl<span class="ansiblue">)</span> <span class="ansiblue">*</span> self<span class="ansiblue">.</span>_linespacing<span class="ansiblue"></span>
   <span class="ansigreen">    354</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, s, prop, ismath)</span>
   <span class="ansigreen">    227</span>             fontsize <span class="ansiblue">=</span> prop<span class="ansiblue">.</span>get_size_in_points<span class="ansiblue">(</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    228</span>             w, h, d = texmanager.get_text_width_height_descent(s, fontsize,
   <span class="ansigreen">--&gt; 229</span><span class="ansired">                                                                renderer=self)
   </span><span class="ansigreen">    230</span>             <span class="ansigreen">return</span> w<span class="ansiblue">,</span> h<span class="ansiblue">,</span> d<span class="ansiblue"></span>
   <span class="ansigreen">    231</span> <span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">get_text_width_height_descent</span><span class="ansiblue">(self, tex, fontsize, renderer)</span>
   <span class="ansigreen">    673</span>         <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    674</span>             <span class="ansired"># use dviread. It sometimes returns a wrong descent.</span><span class="ansiblue"></span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 675</span><span class="ansired">             </span>dvifile <span class="ansiblue">=</span> self<span class="ansiblue">.</span>make_dvi<span class="ansiblue">(</span>tex<span class="ansiblue">,</span> fontsize<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    676</span>             dvi <span class="ansiblue">=</span> dviread<span class="ansiblue">.</span>Dvi<span class="ansiblue">(</span>dvifile<span class="ansiblue">,</span> <span class="ansicyan">72</span> <span class="ansiblue">*</span> dpi_fraction<span class="ansiblue">)</span><span class="ansiblue"></span>
   <span class="ansigreen">    677</span>             <span class="ansigreen">try</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   
   <span class="ansigreen">/usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc</span> in <span class="ansicyan">make_dvi</span><span class="ansiblue">(self, tex, fontsize)</span>
   <span class="ansigreen">    420</span>                      <span class="ansiblue">&apos;string:\n%s\nHere is the full report generated by &apos;</span><span class="ansiblue"></span>
   <span class="ansigreen">    421</span>                      <span class="ansiblue">&apos;LaTeX: \n\n&apos;</span> <span class="ansiblue">%</span> repr<span class="ansiblue">(</span>tex<span class="ansiblue">.</span>encode<span class="ansiblue">(</span><span class="ansiblue">&apos;unicode_escape&apos;</span><span class="ansiblue">)</span><span class="ansiblue">)</span> <span class="ansiblue">+</span><span class="ansiblue"></span>
   <span class="ansigreen">--&gt; 422</span><span class="ansired">                      report))
   </span><span class="ansigreen">    423</span>             <span class="ansigreen">else</span><span class="ansiblue">:</span><span class="ansiblue"></span>
   <span class="ansigreen">    424</span>                 mpl<span class="ansiblue">.</span>verbose<span class="ansiblue">.</span>report<span class="ansiblue">(</span>report<span class="ansiblue">,</span> <span class="ansiblue">&apos;debug&apos;</span><span class="ansiblue">)</span><span class="ansiblue"></span>
   
   <span class="ansired">RuntimeError</span>: LaTeX was not able to process the following string:
   &apos;lp&apos;
   Here is the full report generated by LaTeX: 
   
   </pre>
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   &lt;matplotlib.figure.Figure at 0x7fb773b01990&gt;
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   <p>P-value of the unit-root test, resoundly rejects the null of no unit-root.</p>
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   <div class="input">
   <div class="prompt input_prompt">In&nbsp;[37]:</div>
   <div class="inner_cell">
       <div class="input_area">
   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">sm</span><span class="o">.</span><span class="n">tsa</span><span class="o">.</span><span class="n">adfuller</span><span class="p">(</span><span class="n">cpi</span><span class="p">)[</span><span class="mi">1</span><span class="p">])</span>
   </pre></div>
   
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   0.990432818834
   
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