Autoregressive Moving Average (ARMA): Artificial data
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.. _tsa_arma_1_notebook:

`Link to Notebook GitHub <https://github.com/statsmodels/statsmodels/blob/master/examples/notebooks/tsa_arma_1.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">import</span> <span class="nn">statsmodels.api</span> <span class="kn">as</span> <span class="nn">sm</span>
   <span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
   <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="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">12345</span><span class="p">)</span>
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   <p>Generate some data from an ARMA process:</p>
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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="o">.</span><span class="mi">75</span><span class="p">,</span> <span class="o">-.</span><span class="mi">25</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="o">.</span><span class="mi">65</span><span class="p">,</span> <span class="o">.</span><span class="mi">35</span><span class="p">])</span>
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   <p>The conventions of the arma_generate function require that we specify a 1 for the zero-lag of the AR and MA parameters and that the AR parameters be negated.</p>
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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">r_</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="n">arparams</span><span class="p">]</span>
   <span class="n">maparam</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">maparams</span><span class="p">]</span>
   <span class="n">nobs</span> <span class="o">=</span> <span class="mi">250</span>
   <span class="n">y</span> <span class="o">=</span> <span class="n">arma_generate_sample</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">nobs</span><span class="p">)</span>
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   <p> Now, optionally, we can add some dates information. For this example, we&#39;ll use a pandas time series.</p>
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   <div class="highlight"><pre><span class="n">dates</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">datetools</span><span class="o">.</span><span class="n">dates_from_range</span><span class="p">(</span><span class="s1">&#39;1980m1&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="n">nobs</span><span class="p">)</span>
   <span class="n">y</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">TimeSeries</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">dates</span><span class="p">)</span>
   <span class="n">arma_mod</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">y</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
   <span class="n">arma_res</span> <span class="o">=</span> <span class="n">arma_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trend</span><span class="o">=</span><span class="s1">&#39;nc&#39;</span><span class="p">,</span> <span class="n">disp</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
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   -c:2: FutureWarning: TimeSeries is deprecated. Please use Series
   
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   <div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">arma_res</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span>
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                                 ARMA Model Results                              
   ==============================================================================
   Dep. Variable:                      y   No. Observations:                  250
   Model:                     ARMA(2, 2)   Log Likelihood                -245.887
   Method:                       css-mle   S.D. of innovations              0.645
   Date:                Wed, 27 Apr 2016   AIC                            501.773
   Time:                        01:51:29   BIC                            519.381
   Sample:                    01-31-1980   HQIC                           508.860
                            - 10-31-2000                                         
   ==============================================================================
                    coef    std err          z      P&gt;|z|      [95.0% Conf. Int.]
   ------------------------------------------------------------------------------
   ar.L1.y        0.8411      0.403      2.089      0.038         0.052     1.630
   ar.L2.y       -0.2693      0.247     -1.092      0.276        -0.753     0.214
   ma.L1.y        0.5352      0.412      1.299      0.195        -0.273     1.343
   ma.L2.y        0.0157      0.306      0.051      0.959        -0.585     0.616
                                       Roots                                    
   =============================================================================
                    Real           Imaginary           Modulus         Frequency
   -----------------------------------------------------------------------------
   AR.1            1.5618           -1.1289j            1.9271           -0.0996
   AR.2            1.5618           +1.1289j            1.9271            0.0996
   MA.1           -1.9835           +0.0000j            1.9835            0.5000
   MA.2          -32.1772           +0.0000j           32.1772            0.5000
   -----------------------------------------------------------------------------
   
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   <div class="highlight"><pre><span class="n">y</span><span class="o">.</span><span class="n">tail</span><span class="p">()</span>
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   2000-06-30    0.050999
   2000-07-31   -0.206404
   2000-08-31   -0.170874
   2000-09-30    0.257949
   2000-10-31    0.245237
   dtype: float64
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   <div class="highlight"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
   <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">10</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
   <span class="n">fig</span> <span class="o">=</span> <span class="n">arma_res</span><span class="o">.</span><span class="n">plot_predict</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="s1">&#39;1999m6&#39;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">&#39;2001m5&#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">legend</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">&#39;upper left&#39;</span><span class="p">)</span>
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   Error in callback &lt;function post_execute at 0x7f89c987e578&gt; (for post_execute):
   
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   /build/statsmodels-0.6.1/debian/python-statsmodels/usr/lib/python2.7/dist-packages/statsmodels/tsa/arima_model.py:1724: FutureWarning: TimeSeries is deprecated. Please use Series
     forecast = TimeSeries(forecast, index=self.data.predict_dates)
   
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   <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>
   
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   <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>
   
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   <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>
   
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   <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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   <div class="output_area"><div class="prompt"></div>
   
   
   <div class="output_text output_subarea ">
   <pre>
   &lt;matplotlib.figure.Figure at 0x7f89b7171310&gt;
   </pre>
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