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40 ····················"outputs_hidden":·false40 ····················"outputs_hidden":·false
41 ················}41 ················}
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631 </pre></div></div>631 </pre></div></div>
632 </div>632 </div>
633 <div·class="nboutput·nblast·docutils·container">633 <div·class="nboutput·nblast·docutils·container">
634 <div·class="prompt·empty·docutils·container">634 <div·class="prompt·empty·docutils·container">
635 </div>635 </div>
636 <div·class="output_area·stderr·docutils·container">636 <div·class="output_area·stderr·docutils·container">
637 <div·class="highlight"><pre>637 <div·class="highlight"><pre>
638 /tmp/ipykernel_213045/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use·float(ser.iloc[0])·instead638 /tmp/ipykernel_2634684/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use·float(ser.iloc[0])·instead
639 ··print(&#34;%2.4f%%&#34;·%·(diff*100))639 ··print(&#34;%2.4f%%&#34;·%·(diff*100))
640 </pre></div></div>640 </pre></div></div>
641 </div>641 </div>
642 </section>642 </section>
643 <section·id="Plots">643 <section·id="Plots">
644 <h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3>644 <h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3>
645 <p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p>645 <p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p>
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244 resp_75·=·res.predict(means75)244 resp_75·=·res.predict(means75)
245 diff·=·resp_75·-·resp_25245 diff·=·resp_75·-·resp_25
246 The·interquartile·first·difference·for·the·percentage·of·low·income·households246 The·interquartile·first·difference·for·the·percentage·of·low·income·households
247 in·a·school·district·is:247 in·a·school·district·is:
248 [10]:248 [10]:
249 print("%2.4f%%"·%·(diff*100))249 print("%2.4f%%"·%·(diff*100))
250 -11.8753%250 -11.8753%
251 /tmp/ipykernel_213045/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single251 /tmp/ipykernel_2634684/4175420381.py:1:·FutureWarning:·Calling·float·on·a
252 element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use252 single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.
253 float(ser.iloc[0])·instead253 Use·float(ser.iloc[0])·instead
254 ··print("%2.4f%%"·%·(diff*100))254 ··print("%2.4f%%"·%·(diff*100))
255 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*255 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
256 We·extract·information·that·will·be·used·to·draw·some·interesting·plots:256 We·extract·information·that·will·be·used·to·draw·some·interesting·plots:
257 [11]:257 [11]:
258 nobs·=·res.nobs258 nobs·=·res.nobs
259 y·=·data.endog.iloc[:,0]/data.endog.sum(1)259 y·=·data.endog.iloc[:,0]/data.endog.sum(1)
260 yhat·=·res.mu260 yhat·=·res.mu
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34 ····················"shell.execute_reply":·"2025-05-23T07:44:27.279971Z"34 ····················"shell.execute_reply":·"2024-04-20T04:00:55.910706Z"
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38 ············"source":·[38 ············"source":·[
39 ················"import·numpy·as·np\n",39 ················"import·numpy·as·np\n",
40 ················"import·statsmodels.api·as·sm\n",40 ················"import·statsmodels.api·as·sm\n",
41 ················"from·scipy·import·stats\n",41 ················"from·scipy·import·stats\n",
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486 </pre></div></div>486 </pre></div></div>
487 </div>487 </div>
488 <div·class="nboutput·nblast·docutils·container">488 <div·class="nboutput·nblast·docutils·container">
489 <div·class="prompt·empty·docutils·container">489 <div·class="prompt·empty·docutils·container">
490 </div>490 </div>
491 <div·class="output_area·stderr·docutils·container">491 <div·class="output_area·stderr·docutils·container">
492 <div·class="highlight"><pre>492 <div·class="highlight"><pre>
493 /tmp/ipykernel_212941/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`493 /tmp/ipykernel_2634385/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
494 ··print(mod1.params[1])494 ··print(mod1.params[1])
495 /tmp/ipykernel_212941/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`495 /tmp/ipykernel_2634385/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
496 ··print(mod2.params[1]·*·2)496 ··print(mod2.params[1]·*·2)
497 </pre></div></div>497 </pre></div></div>
498 </div>498 </div>
499 </section>499 </section>
  
  
500 ············<div·class="clearer"></div>500 ············<div·class="clearer"></div>
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176 As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half176 As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half
177 the·size·of·the·LOWINC·coefficient·from·the·first·model:177 the·size·of·the·LOWINC·coefficient·from·the·first·model:
178 [4]:178 [4]:
179 print(mod1.params[1])179 print(mod1.params[1])
180 print(mod2.params[1]·*·2)180 print(mod2.params[1]·*·2)
181 -0.020395987154756403181 -0.020395987154756403
182 -0.020395987154757343182 -0.020395987154757343
183 /tmp/ipykernel_212941/1000445862.py:1:·FutureWarning:·Series.__getitem__183 /tmp/ipykernel_2634385/1000445862.py:1:·FutureWarning:·Series.__getitem__
184 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys184 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
185 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To185 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
186 access·a·value·by·position,·use·`ser.iloc[pos]`186 access·a·value·by·position,·use·`ser.iloc[pos]`
187 ··print(mod1.params[1])187 ··print(mod1.params[1])
188 /tmp/ipykernel_212941/1000445862.py:2:·FutureWarning:·Series.__getitem__188 /tmp/ipykernel_2634385/1000445862.py:2:·FutureWarning:·Series.__getitem__
189 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys189 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
190 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To190 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
191 access·a·value·by·position,·use·`ser.iloc[pos]`191 access·a·value·by·position,·use·`ser.iloc[pos]`
192 ··print(mod2.params[1]·*·2)192 ··print(mod2.params[1]·*·2)
193 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8]193 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8]
194 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*194 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*
195 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s195 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
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23 ················"import·numpy·as·np\n",23 ················"import·numpy·as·np\n",
24 ················"import·pandas·as·pd\n",24 ················"import·pandas·as·pd\n",
25 ················"import·statsmodels.formula.api·as·smf\n",25 ················"import·statsmodels.formula.api·as·smf\n",
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799 </div>799 </div>
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126 lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)126 lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)
127 ax.set_xticklabels(dta.columns.values[::10])127 ax.set_xticklabels(dta.columns.values[::10])
128 ax.set_xlim(0,·51)128 ax.set_xlim(0,·51)
129 ax.set_xlabel("Year",·size=17)129 ax.set_xlabel("Year",·size=17)
130 fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)130 fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)
131 legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")131 legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")
132 legend.draw_frame(False)132 legend.draw_frame(False)
133 /tmp/ipykernel_209649/427128218.py:3:·UserWarning:·FixedFormatter·should·only133 /tmp/ipykernel_2630258/427128218.py:3:·UserWarning:·FixedFormatter·should·only
134 be·used·together·with·FixedLocator134 be·used·together·with·FixedLocator
135 ··ax.set_xticklabels(dta.columns.values[::10])135 ··ax.set_xticklabels(dta.columns.values[::10])
136 [../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]136 [../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]
137 To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories137 To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories
138 for·sets·of·countries·with·similar·PC·scores.·The·following·convenience138 for·sets·of·countries·with·similar·PC·scores.·The·following·convenience
139 function·produces·such·a·plot.139 function·produces·such·a·plot.
140 [8]:140 [8]:
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30 ················"execution":·{30 ················"execution":·{
31 ····················"iopub.execute_input":·"2025-05-23T07:43:56.393187Z",31 ····················"iopub.execute_input":·"2024-04-20T04:00:34.317875Z",
32 ····················"iopub.status.busy":·"2025-05-23T07:43:56.392786Z",32 ····················"iopub.status.busy":·"2024-04-20T04:00:34.317381Z",
33 ····················"iopub.status.idle":·"2025-05-23T07:43:58.336805Z",33 ····················"iopub.status.idle":·"2024-04-20T04:00:35.422432Z",
34 ····················"shell.execute_reply":·"2025-05-23T07:43:58.335963Z"34 ····················"shell.execute_reply":·"2024-04-20T04:00:35.421555Z"
35 ················}35 ················}
36 ············},36 ············},
37 ············"outputs":·[],37 ············"outputs":·[],
38 ············"source":·[38 ············"source":·[
39 ················"from·statsmodels.compat·import·lmap\n",39 ················"from·statsmodels.compat·import·lmap\n",
40 ················"import·numpy·as·np\n",40 ················"import·numpy·as·np\n",
41 ················"from·scipy·import·stats\n",41 ················"from·scipy·import·stats\n",
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578 </pre></div></div>578 </pre></div></div>
579 </div>579 </div>
580 <div·class="nboutput·nblast·docutils·container">580 <div·class="nboutput·nblast·docutils·container">
581 <div·class="prompt·empty·docutils·container">581 <div·class="prompt·empty·docutils·container">
582 </div>582 </div>
583 <div·class="output_area·stderr·docutils·container">583 <div·class="output_area·stderr·docutils·container">
584 <div·class="highlight"><pre>584 <div·class="highlight"><pre>
585 /tmp/ipykernel_208001/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`585 /tmp/ipykernel_2626778/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
586 ··print(&#39;var.level·····=·%.5f&#39;·%·res.params[0])586 ··print(&#39;var.level·····=·%.5f&#39;·%·res.params[0])
587 /tmp/ipykernel_208001/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`587 /tmp/ipykernel_2626778/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
588 ··print(&#39;var.irregular·=·%.5f&#39;·%·res.params[1])588 ··print(&#39;var.irregular·=·%.5f&#39;·%·res.params[1])
589 /tmp/ipykernel_208001/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`589 /tmp/ipykernel_2626778/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
590 ··print(&#39;h·*·scale·····=·%.5f&#39;·%·(res_conc.params[0]·*·res_conc.scale))590 ··print(&#39;h·*·scale·····=·%.5f&#39;·%·(res_conc.params[0]·*·res_conc.scale))
591 </pre></div></div>591 </pre></div></div>
592 </div>592 </div>
593 </section>593 </section>
594 </section>594 </section>
595 <section·id="Example:-SARIMAX">595 <section·id="Example:-SARIMAX">
596 <h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>596 <h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>
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242 Original·model242 Original·model
243 var.level·····=·0.74469243 var.level·····=·0.74469
244 var.irregular·=·3.37330244 var.irregular·=·3.37330
  
245 Concentrated·model245 Concentrated·model
246 scale·········=·0.74472246 scale·········=·0.74472
247 h·*·scale·····=·3.37338247 h·*·scale·····=·3.37338
248 /tmp/ipykernel_208001/976557282.py:2:·FutureWarning:·Series.__getitem__248 /tmp/ipykernel_2626778/976557282.py:2:·FutureWarning:·Series.__getitem__
249 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys249 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
250 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To250 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
251 access·a·value·by·position,·use·`ser.iloc[pos]`251 access·a·value·by·position,·use·`ser.iloc[pos]`
252 ··print('var.level·····=·%.5f'·%·res.params[0])252 ··print('var.level·····=·%.5f'·%·res.params[0])
253 /tmp/ipykernel_208001/976557282.py:3:·FutureWarning:·Series.__getitem__253 /tmp/ipykernel_2626778/976557282.py:3:·FutureWarning:·Series.__getitem__
254 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys254 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
255 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To255 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
256 access·a·value·by·position,·use·`ser.iloc[pos]`256 access·a·value·by·position,·use·`ser.iloc[pos]`
257 ··print('var.irregular·=·%.5f'·%·res.params[1])257 ··print('var.irregular·=·%.5f'·%·res.params[1])
258 /tmp/ipykernel_208001/976557282.py:7:·FutureWarning:·Series.__getitem__258 /tmp/ipykernel_2626778/976557282.py:7:·FutureWarning:·Series.__getitem__
259 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys259 treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
260 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To260 will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
261 access·a·value·by·position,·use·`ser.iloc[pos]`261 access·a·value·by·position,·use·`ser.iloc[pos]`
262 ··print('h·*·scale·····=·%.5f'·%·(res_conc.params[0]·*·res_conc.scale))262 ··print('h·*·scale·····=·%.5f'·%·(res_conc.params[0]·*·res_conc.scale))
263 *\x8**\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*263 *\x8**\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
264 By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically264 By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically
265 maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow265 maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow
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19 ················}19 ················}
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21 ············"outputs":·[],21 ············"outputs":·[],
22 ············"source":·[22 ············"source":·[
23 ················"import·numpy·as·np\n",23 ················"import·numpy·as·np\n",
24 ················"import·pandas·as·pd\n",24 ················"import·pandas·as·pd\n",
25 ················"import·statsmodels.api·as·sm\n",25 ················"import·statsmodels.api·as·sm\n",
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388 </div>388 </div>
389 </div>389 </div>
390 <div·class="nboutput·nblast·docutils·container">390 <div·class="nboutput·nblast·docutils·container">
391 <div·class="prompt·empty·docutils·container">391 <div·class="prompt·empty·docutils·container">
392 </div>392 </div>
393 <div·class="output_area·docutils·container">393 <div·class="output_area·docutils·container">
394 <div·class="highlight"><pre>394 <div·class="highlight"><pre>
395 ·······························SARIMAX·Results 
396 ============================================================================== 
397 Dep.·Variable:···················infl···No.·Observations:··················203 
398 Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714 
399 Date:················Sun,·21·Jan·2024···AIC····························951.427 
400 Time:························09:38:29···BIC····························961.367 
401 Sample:····················03-31-1959···HQIC···························955.449 
402 ·························-·09-30-2009 
403 Covariance·Type:··················opg 
404 ============================================================================== 
405 ·················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
406 ------------------------------------------------------------------------------ 
407 intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895 
408 ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721 
409 sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930 
410 =================================================================================== 
411 Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB):················68.45 
412 Prob(Q):······························0.00···Prob(JB):·························0.00 
413 Heteroskedasticity·(H):···············1.47···Skew:····························-0.22 
414 Prob(H)·(two-sided):··················0.12···Kurtosis:·························5.81 
415 =================================================================================== 
  
416 Warnings: 
417 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex-step). 
418 RUNNING·THE·L-BFGS-B·CODE395 RUNNING·THE·L-BFGS-B·CODE
  
419 ···········*·*·*396 ···········*·*·*
  
420 Machine·precision·=·2.220D-16397 Machine·precision·=·2.220D-16
421 ·N·=············3·····M·=···········10398 ·N·=············3·····M·=···········10
422 ·This·problem·is·unconstrained.399 ·This·problem·is·unconstrained.
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42 [3]:42 [3]:
43 #·Construct·the·model43 #·Construct·the·model
44 mod·=·sm.tsa.SARIMAX(endog,·order=(1,·0,·0),·trend='c')44 mod·=·sm.tsa.SARIMAX(endog,·order=(1,·0,·0),·trend='c')
45 #·Estimate·the·parameters45 #·Estimate·the·parameters
46 res·=·mod.fit()46 res·=·mod.fit()
  
47 print(res.summary())47 print(res.summary())
48 ·······························SARIMAX·Results 
49 ============================================================================== 
50 Dep.·Variable:···················infl···No.·Observations:··················203 
51 Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714 
52 Date:················Sun,·21·Jan·2024···AIC····························951.427 
53 Time:························09:38:29···BIC····························961.367 
54 Sample:····················03-31-1959···HQIC···························955.449 
55 ·························-·09-30-2009 
56 Covariance·Type:··················opg 
57 ============================================================================== 
58 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
59 ------------------------------------------------------------------------------ 
60 intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895 
61 ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721 
62 sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930 
63 =================================================================================== 
64 Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB): 
65 68.45 
66 Prob(Q):······························0.00···Prob(JB): 
67 0.00 
68 Heteroskedasticity·(H):···············1.47···Skew:····························- 
69 0.22 
70 Prob(H)·(two-sided):··················0.12···Kurtosis: 
71 5.81 
72 =================================================================================== 
  
73 Warnings: 
74 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex- 
75 step). 
76 RUNNING·THE·L-BFGS-B·CODE48 RUNNING·THE·L-BFGS-B·CODE
  
77 ···········*·*·*49 ···········*·*·*
  
78 Machine·precision·=·2.220D-1650 Machine·precision·=·2.220D-16
79 ·N·=············3·····M·=···········1051 ·N·=············3·····M·=···········10
80 ·This·problem·is·unconstrained.52 ·This·problem·is·unconstrained.
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581 </pre></div></div>581 </pre></div></div>
582 </div>582 </div>
583 <div·class="nboutput·nblast·docutils·container">583 <div·class="nboutput·nblast·docutils·container">
584 <div·class="prompt·empty·docutils·container">584 <div·class="prompt·empty·docutils·container">
585 </div>585 </div>
586 <div·class="output_area·stderr·docutils·container">586 <div·class="output_area·stderr·docutils·container">
587 <div·class="highlight"><pre>587 <div·class="highlight"><pre>
588 /tmp/ipykernel_204151/1512460390.py:6:·InterpolationWarning:·The·test·statistic·is·outside·of·the·range·of·p-values·available·in·the588 /tmp/ipykernel_2622017/1512460390.py:6:·InterpolationWarning:·The·test·statistic·is·outside·of·the·range·of·p-values·available·in·the
589 look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned.589 look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned.
  
590 ··kpsstest·=·kpss(timeseries,·regression=&#34;c&#34;,·nlags=&#34;auto&#34;)590 ··kpsstest·=·kpss(timeseries,·regression=&#34;c&#34;,·nlags=&#34;auto&#34;)
591 </pre></div></div>591 </pre></div></div>
592 </div>592 </div>
593 <p>Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected.·Hence,·the·series·is·stationary.</p>593 <p>Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected.·Hence,·the·series·is·stationary.</p>
594 </section>594 </section>
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172 p-value··················0.100000172 p-value··················0.100000
173 Lags·Used················0.000000173 Lags·Used················0.000000
174 Critical·Value·(10%)·····0.347000174 Critical·Value·(10%)·····0.347000
175 Critical·Value·(5%)······0.463000175 Critical·Value·(5%)······0.463000
176 Critical·Value·(2.5%)····0.574000176 Critical·Value·(2.5%)····0.574000
177 Critical·Value·(1%)······0.739000177 Critical·Value·(1%)······0.739000
178 dtype:·float64178 dtype:·float64
179 /tmp/ipykernel_204151/1512460390.py:6:·InterpolationWarning:·The·test·statistic179 /tmp/ipykernel_2622017/1512460390.py:6:·InterpolationWarning:·The·test
180 is·outside·of·the·range·of·p-values·available·in·the180 statistic·is·outside·of·the·range·of·p-values·available·in·the
181 look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned.181 look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned.
  
182 ··kpsstest·=·kpss(timeseries,·regression="c",·nlags="auto")182 ··kpsstest·=·kpss(timeseries,·regression="c",·nlags="auto")
183 Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected.183 Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected.
184 Hence,·the·series·is·stationary.184 Hence,·the·series·is·stationary.
185 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nc\x8cl\x8lu\x8us\x8si\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*185 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nc\x8cl\x8lu\x8us\x8si\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
186 Two·tests·for·checking·the·stationarity·of·a·time·series·are·used,·namely·ADF186 Two·tests·for·checking·the·stationarity·of·a·time·series·are·used,·namely·ADF
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38 ················"import·numpy·as·np\n",38 ················"import·numpy·as·np\n",
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889 </div>889 </div>
890 </div>890 </div>
891 <div·class="nboutput·docutils·container">891 <div·class="nboutput·docutils·container">
892 <div·class="prompt·empty·docutils·container">892 <div·class="prompt·empty·docutils·container">
893 </div>893 </div>
894 <div·class="output_area·docutils·container">894 <div·class="output_area·docutils·container">
895 <div·class="highlight"><pre>895 <div·class="highlight"><pre>
896 410·ms·±·84.9·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·each)896 174·ms·±·23.3·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)
897 </pre></div></div>897 </pre></div></div>
898 </div>898 </div>
899 <div·class="nboutput·nblast·docutils·container">899 <div·class="nboutput·nblast·docutils·container">
900 <div·class="prompt·empty·docutils·container">900 <div·class="prompt·empty·docutils·container">
901 </div>901 </div>
902 <div·class="output_area·docutils·container">902 <div·class="output_area·docutils·container">
903 <img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png"·/>903 <img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png"·/>
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493 [../../../_images/examples_notebooks_generated_stl_decomposition_15_0.png]493 [../../../_images/examples_notebooks_generated_stl_decomposition_15_0.png]
494 First,·the·base·line·model·is·estimated·with·all·jumps·equal·to·1.494 First,·the·base·line·model·is·estimated·with·all·jumps·equal·to·1.
495 [10]:495 [10]:
496 mod·=·STL(y,·period=period,·seasonal=seasonal)496 mod·=·STL(y,·period=period,·seasonal=seasonal)
497 %timeit·mod.fit()497 %timeit·mod.fit()
498 res·=·mod.fit()498 res·=·mod.fit()
499 fig·=·res.plot(observed=False,·resid=False)499 fig·=·res.plot(observed=False,·resid=False)
500 410·ms·±·84.9·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·each)500 174·ms·±·23.3·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)
501 [../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png]501 [../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png]
502 The·jumps·are·all·set·to·15%·of·their·window·length.·Limited·linear502 The·jumps·are·all·set·to·15%·of·their·window·length.·Limited·linear
503 interpolation·makes·little·difference·to·the·fit·of·the·model.503 interpolation·makes·little·difference·to·the·fit·of·the·model.
504 [11]:504 [11]:
505 low_pass_jump·=·seasonal_jump·=·int(0.15·*·(period·+·1))505 low_pass_jump·=·seasonal_jump·=·int(0.15·*·(period·+·1))
506 trend_jump·=·int(0.15·*·1.5·*·(period·+·1))506 trend_jump·=·int(0.15·*·1.5·*·(period·+·1))
507 mod·=·STL(507 mod·=·STL(
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389 ········"mai":·[3,·4,·5,·34,·51,·81,·113,·174,·177,·183,·185,·188,·190,·191,·193,·194,·196,·197,·198,·199,·201,·203,·206,·207,·208,·209,·210,·211,·215,·217,·220,·221,·222,·226,·227,·228,·229,·231,·232,·233,·234,·237,·238,·241,·243,·244,·245,·246,·248,·249,·250,·251,·252,·253,·254,·257,·259,·261,·263,·265,·266[·...·truncated·by·diffoscope;·len:·2195,·SHA:·ef359efb75996afe33154dbd3014908d2717462617bf8e0113d7c484d2668884·...·],·6432,·6433,·6435,·6437,·6439,·6440,·6441,·6442,·6444,·6445,·6446,·6447,·6448,·6449,·6450,·6454,·6455,·6460],389 ········"mai":·[3,·4,·5,·34,·51,·81,·113,·174,·177,·185,·188,·190,·191,·194,·206,·215,·220,·221,·222,·226,·228,·237,·241,·243,·244,·245,·248,·249,·250,·251,·252,·253,·254,·263,·266,·269,·270,·271,·272,·284,·356,·425,·483,·541,·598,·653,·707,·768,·831,·847,·910,·990,·1074,·1130,·1204,·1244,·1279,·1356,·1357,·1[·...·truncated·by·diffoscope;·len:·2031,·SHA:·ea360878ef49ac36e21fb99f73441e2e685828e90221b813317930fb2ec194f9·...·],·6432,·6433,·6435,·6437,·6439,·6440,·6441,·6442,·6444,·6445,·6446,·6447,·6448,·6449,·6450,·6454,·6455,·6460],
390 ········"includ":·[3,·4,·11,·12,·13,·17,·24,·26,·27,·30,·31,·39,·45,·59,·90,·121,·122,·173,·175,·177,·178,·179,·183,·185,·188,·190,·191,·194,·196,·197,·198,·202,·203,·205,·207,·211,·216,·217,·219,·220,·223,·225,·226,·231,·232,·235,·237,·238,·239,·242,·243,·244,·245,·246,·249,·251,·252,·253,·257,·259,·260,·267,·292,·307,·364,·365,·382,·401,·402,·439,·440,·459,·460,·497,·498,·517,·518,·555,·574,·575,·612,·629,·630,·667,·684,·685,·720,·721,·782,·783,·807,·808,·846,·847,·924,·925,·942,·1004,·1005,·1027,·1050,·1051,·1089,·1090,·1106,·1107,·1144,·1145,·1162,·1180,·1181,·1218,·1220,·1221,·1258,·1259,·1284,·1357,·1366,·1376,·1379,·1402,·1452,·1491,·1503,·1521,·1550,·1587,·1613,·1628,·1631,·1644,·1647,·1687,·1919,·1927,·1940,·1970,·1971,·1985,·2016,·2017,·2025,·2038,·2046,·2054,·2067,·2075,·2091,·2111,·2112,·2146,·2186,·2196,·2198,·2208,·2221,·2223,·2224,·2237,·2238,·2248,·2251,·2299,·2318,·2336,·2351,·2355,·2412,·2416,·2453,·2461,·2466,·2471,·2480,·2481,·2482,·2484,·2497,·2545,·2548,·2610,·2634,·2635,·2639,·2651,·2652,·2656,·2669,·2670,·2674,·2686,·2699,·2716,·2725,·2731,·2732,·2744,·2754,·2767,·2781,·2795,·2796,·2808,·2810,·2811,·2815,·2827,·2832,·2834,·2884,·2889,·2898,·2934,·2936,·2963,·2977,·3006,·3012,·3019,·3033,·3043,·3044,·3053,·3056,·3057,·3072,·3075,·3076,·3077,·3098,·3100,·3117,·3122,·3124,·3127,·3135,·3152,·3153,·3159,·3208,·3246,·3262,·3271,·3287,·3296,·3312,·3321,·3337,·3346,·3368,·3377,·3393,·3402,·3424,·3433,·3449,·3458,·3481,·3522,·3523,·3539,·3586,·3587,·3600,·3614,·3628,·3629,·3642,·3644,·3648,·3666,·3670,·3738,·3746,·3750,·3751,·3752,·3760,·3762,·3764,·3773,·3783,·3815,·3871,·3888,·3896,·3898,·3899,·3904,·3906,·3910,·3917,·3918,·3924,·3931,·3934,·3943,·3947,·3951,·3952,·3953,·3957,·3971,·3974,·3980,·3990,·3994,·4000,·4002,·4004,·4006,·4010,·4011,·4016,·4024,·4026,·4027,·4042,·4043,·4057,·4091,·4115,·4117,·4121,·4140,·4141,·4142,·4143,·4144,·4167,·4172,·4173,·4174,·4229,·4230,·4231,·4232,·4234,·4235,·4236,·4237,·4276,·4277,·4281,·4294,·4299,·4320,·4321,·4333,·4335,·4339,·4340,·4341,·4342,·4347,·4349,·4352,·4363,·4365,·4371,·4372,·4373,·4378,·4399,·4400,·4412,·4414,·4418,·4427,·4428,·4433,·4435,·4438,·4439,·4450,·4455,·4458,·4485,·4486,·4498,·4500,·4504,·4505,·4506,·4510,·4511,·4517,·4539,·4540,·4551,·4552,·4561,·4564,·4565,·4567,·4579,·4582,·4583,·4584,·4596,·4601,·4602,·4607,·4608,·4617,·4621,·4623,·4624,·4625,·4629,·4638,·4640,·4643,·4644,·4645,·4647,·4652,·4653,·4669,·4673,·4681,·4683,·4690,·4696,·4701,·4704,·4707,·4710,·4719,·4720,·4726,·4727,·4732,·4748,·4793,·4797,·4804,·4830,·4834,·4837,·4842,·4855,·4890,·4896,·4911,·4921,·4936,·4949,·4961,·4966,·4970,·4971,·4977,·4991,·5001,·5002,·5011,·5014,·5015,·5027,·5031,·5032,·5033,·5047,·5048,·5049,·5062,·5066,·5068,·5073,·5074,·5081,·5107,·5108,·5121,·5122,·5134,·5138,·5140,·5141,·5153,·5155,·5156,·5157,·5170,·5174,·5176,·5180,·5181,·5187,·5202,·5212,·5213,·5225,·5226,·5237,·5240,·5241,·5242,·5256,·5257,·5270,·5274,·5290,·5305,·5346,·5387,·5402,·5442,·5443,·5445,·5446,·5476,·5481,·5491,·5492,·5498,·5512,·5522,·5523,·5535,·5536,·5547,·5550,·5551,·5552,·5566,·5567,·5580,·5584,·5595,·5599,·5605,·5606,·5607,·5608,·5609,·5610,·5621,·5637,·5641,·5642,·5648,·5670,·5671,·5682,·5683,·5692,·5695,·5696,·5698,·5710,·5713,·5714,·5715,·5727,·5732,·5733,·5738,·5739,·5748,·5752,·5754,·5775,·5790,·5791,·5831,·5832,·5834,·5836,·5838,·5865,·5869,·5870,·5876,·5891,·5902,·5903,·5912,·5915,·5916,·5929,·5932,·5934,·5935,·5950,·5951,·5952,·5967,·5972,·5983,·5987,·5988,·5994,·6008,·6018,·6019,·6028,·6031,·6032,·6043,·6046,·6047,·6048,·6062,·6063,·6076,·6080,·6082,·6084,·6090,·6091,·6092,·6095,·6097,·6098,·6103,·6104,·6107,·6108,·6133,·6134,·6135,·6159,·6162,·6173,·6176,·6178,·6185,·6191,·6217,·6218,·6224,·6234,·6260,·6263,·6274,·6278,·6285,·6291,·6317,·6318,·6324,·6332,·6380,·6410,·6411,·6413,·6418,·6423,·6424,·6425,·6431,·6432,·6435,·6437,·6439,·6444,·6445,·6446,·6447,·6448,·6449,·6450,·6453,·6454,·6455,·6458],390 ········"includ":·[3,·4,·11,·12,·13,·17,·24,·26,·27,·30,·31,·39,·45,·59,·90,·121,·122,·173,·175,·177,·178,·179,·183,·185,·188,·190,·191,·194,·196,·197,·198,·202,·203,·205,·207,·211,·216,·217,·219,·220,·223,·225,·226,·231,·232,·235,·237,·238,·239,·242,·243,·244,·245,·246,·249,·251,·252,·253,·257,·259,·260,·267,·292,·307,·364,·365,·382,·401,·402,·439,·440,·459,·460,·497,·498,·517,·518,·555,·574,·575,·612,·629,·630,·667,·684,·685,·720,·721,·782,·783,·807,·808,·846,·847,·924,·925,·942,·1004,·1005,·1027,·1050,·1051,·1089,·1090,·1106,·1107,·1144,·1145,·1162,·1180,·1181,·1218,·1220,·1221,·1258,·1259,·1284,·1357,·1366,·1376,·1379,·1402,·1452,·1491,·1503,·1521,·1550,·1587,·1613,·1628,·1631,·1644,·1647,·1687,·1919,·1927,·1940,·1970,·1971,·1985,·2016,·2017,·2025,·2038,·2046,·2054,·2067,·2075,·2091,·2111,·2112,·2146,·2186,·2196,·2198,·2208,·2221,·2223,·2224,·2237,·2238,·2248,·2251,·2299,·2318,·2336,·2351,·2355,·2412,·2416,·2453,·2461,·2466,·2471,·2480,·2481,·2482,·2484,·2497,·2545,·2548,·2610,·2634,·2635,·2639,·2651,·2652,·2656,·2669,·2670,·2674,·2686,·2699,·2716,·2725,·2731,·2732,·2744,·2754,·2767,·2781,·2795,·2796,·2808,·2810,·2811,·2815,·2827,·2832,·2834,·2884,·2889,·2898,·2934,·2936,·2963,·2977,·3006,·3012,·3019,·3033,·3043,·3044,·3053,·3056,·3057,·3072,·3075,·3076,·3077,·3098,·3100,·3117,·3122,·3124,·3127,·3135,·3152,·3153,·3159,·3208,·3246,·3262,·3271,·3287,·3296,·3312,·3321,·3337,·3346,·3368,·3377,·3393,·3402,·3424,·3433,·3449,·3458,·3481,·3522,·3523,·3539,·3586,·3587,·3600,·3614,·3628,·3629,·3642,·3644,·3648,·3666,·3670,·3738,·3746,·3750,·3751,·3752,·3760,·3762,·3764,·3773,·3783,·3815,·3871,·3888,·3896,·3898,·3899,·3904,·3906,·3910,·3917,·3918,·3924,·3931,·3934,·3943,·3947,·3951,·3952,·3953,·3957,·3971,·3974,·3980,·3990,·3994,·4000,·4002,·4004,·4006,·4010,·4011,·4016,·4024,·4026,·4027,·4042,·4043,·4057,·4091,·4115,·4117,·4121,·4140,·4141,·4142,·4143,·4144,·4167,·4172,·4173,·4174,·4229,·4230,·4231,·4232,·4234,·4235,·4236,·4237,·4276,·4277,·4281,·4294,·4299,·4320,·4321,·4333,·4335,·4339,·4340,·4341,·4342,·4347,·4349,·4352,·4363,·4365,·4371,·4372,·4373,·4378,·4399,·4400,·4412,·4414,·4418,·4427,·4428,·4433,·4435,·4438,·4439,·4450,·4455,·4458,·4485,·4486,·4498,·4500,·4504,·4505,·4506,·4510,·4511,·4517,·4539,·4540,·4551,·4552,·4561,·4564,·4565,·4567,·4579,·4582,·4583,·4584,·4596,·4601,·4602,·4607,·4608,·4617,·4621,·4623,·4624,·4625,·4629,·4638,·4640,·4643,·4644,·4645,·4647,·4652,·4653,·4669,·4673,·4681,·4683,·4690,·4696,·4701,·4704,·4707,·4710,·4719,·4720,·4726,·4727,·4732,·4748,·4793,·4797,·4804,·4830,·4834,·4837,·4842,·4855,·4890,·4896,·4911,·4921,·4936,·4949,·4961,·4966,·4970,·4971,·4977,·4991,·5001,·5002,·5011,·5014,·5015,·5027,·5031,·5032,·5033,·5047,·5048,·5049,·5062,·5066,·5068,·5073,·5074,·5081,·5107,·5108,·5121,·5122,·5134,·5138,·5140,·5141,·5153,·5155,·5156,·5157,·5170,·5174,·5176,·5180,·5181,·5187,·5202,·5212,·5213,·5225,·5226,·5237,·5240,·5241,·5242,·5256,·5257,·5270,·5274,·5290,·5305,·5346,·5387,·5402,·5442,·5443,·5445,·5446,·5476,·5481,·5491,·5492,·5498,·5512,·5522,·5523,·5535,·5536,·5547,·5550,·5551,·5552,·5566,·5567,·5580,·5584,·5595,·5599,·5605,·5606,·5607,·5608,·5609,·5610,·5621,·5637,·5641,·5642,·5648,·5670,·5671,·5682,·5683,·5692,·5695,·5696,·5698,·5710,·5713,·5714,·5715,·5727,·5732,·5733,·5738,·5739,·5748,·5752,·5754,·5775,·5790,·5791,·5831,·5832,·5834,·5836,·5838,·5865,·5869,·5870,·5876,·5891,·5902,·5903,·5912,·5915,·5916,·5929,·5932,·5934,·5935,·5950,·5951,·5952,·5967,·5972,·5983,·5987,·5988,·5994,·6008,·6018,·6019,·6028,·6031,·6032,·6043,·6046,·6047,·6048,·6062,·6063,·6076,·6080,·6082,·6084,·6090,·6091,·6092,·6095,·6097,·6098,·6103,·6104,·6107,·6108,·6133,·6134,·6135,·6159,·6162,·6173,·6176,·6178,·6185,·6191,·6217,·6218,·6224,·6234,·6260,·6263,·6274,·6278,·6285,·6291,·6317,·6318,·6324,·6332,·6380,·6410,·6411,·6413,·6418,·6423,·6424,·6425,·6431,·6432,·6435,·6437,·6439,·6444,·6445,·6446,·6447,·6448,·6449,·6450,·6453,·6454,·6455,·6458],
391 ········"find":·[3,·177,·179,·182,·185,·187,·202,·216,·226,·231,·238,·240,·241,·248,·251,·257,·266,·1472,·1473,·1527,·1528,·1622,·1626,·1627,·1638,·1642,·1643,·2195,·2196,·2431,·2544,·2700,·3207,·3731,·3732,·3738,·3777,·3881,·3882,·3883,·3885,·3924,·3928,·4087,·4088,·4091,·4095,·4099,·4103,·4107,·4110,·4111,·4112,·4130,·4290,·4312,·4321,·4322,·4359,·4391,·4400,·4401,·4446,·4477,·4486,·4487,·4633,·4640,·4646,·4804,·4837,·4850,·4885,·4943,·6409,·6410,·6411,·6447,·6454,·6455],391 ········"find":·[3,·177,·179,·182,·185,·187,·202,·216,·226,·231,·238,·240,·241,·248,·251,·257,·266,·1472,·1473,·1527,·1528,·1622,·1626,·1627,·1638,·1642,·1643,·2195,·2196,·2431,·2544,·2700,·3207,·3731,·3732,·3738,·3777,·3881,·3882,·3883,·3885,·3924,·3928,·4087,·4088,·4091,·4095,·4099,·4103,·4107,·4110,·4111,·4112,·4130,·4290,·4312,·4321,·4322,·4359,·4391,·4400,·4401,·4446,·4477,·4486,·4487,·4633,·4640,·4646,·4804,·4837,·4850,·4885,·4943,·6409,·6410,·6411,·6447,·6454,·6455],
392 ········"someth":·[3,·174,·177,·178,·179,·239,·2080,·3357,·3725,·3742,·3744,·6419,·6421,·6446],392 ········"someth":·[3,·174,·177,·178,·179,·239,·2080,·3357,·3725,·3742,·3744,·6419,·6421,·6446],
393 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./usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_14_2.png vs.
./usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_ets_14_3.png
Files identical despite different names