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/srv/reproducible-results/rbuild-debian/r-b-build.nDXZhPvq/b2/statsmodels_0.14.2+dfsg-1_arm64.changes ¶

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python-statsmodels-doc_0.14.2+dfsg-1_all.deb ¶

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file list ¶

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control.tar.xz ¶

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control.tar ¶

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./control ¶

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./md5sums ¶

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line order ¶

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data.tar.xz ¶

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data.tar ¶

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199	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_24_0.png	199	usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_exponential_smoothing_24_0.png


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53	················"import·matplotlib.pyplot·as·plt\n",	53	················"import·matplotlib.pyplot·as·plt\n",
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158	············"cell_type":·"code",	158	············"cell_type":·"code",
159	············"execution_count":·6,	159	············"execution_count":·6,
160	············"metadata":·{	160	············"metadata":·{
161	················"execution":·{	161	················"execution":·{
162	····················"iopub.execute_input":·"2024-05-26T09:39:32.~~402805~~Z",	162	····················"iopub.execute_input":·"2024-05-26T12:10:08.924469Z",
163	····················"iopub.status.busy":·"2024-05-26T09:39:32.402490Z",	163	····················"iopub.status.busy":·"2024-05-26T12:10:08.924143Z",
164	····················"iopub.status.idle":·"2024-05-26T09:39:32.442667Z",	164	····················"iopub.status.idle":·"2024-05-26T12:10:08.956071Z",
165	····················"shell.execute_reply":·"2024-05-26T09:39:32.441597Z"	165	····················"shell.execute_reply":·"2024-05-26T12:10:08.955379Z"
166	················}	166	················}
167	············},	167	············},
168	············"outputs":·[	168	············"outputs":·[
169	················{	169	················{
170	····················"name":·"stdout",	170	····················"name":·"stdout",
171	····················"output_type":·"stream",	171	····················"output_type":·"stream",
172	····················"text":·[	172	····················"text":·[
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202	············]	202	············]
203	········},	203	········},
204	········{	204	········{
205	············"cell_type":·"code",	205	············"cell_type":·"code",
206	············"execution_count":·7,	206	············"execution_count":·7,
207	············"metadata":·{	207	············"metadata":·{
208	················"execution":·{	208	················"execution":·{
209	····················"iopub.execute_input":·"2024-05-26T09:39:32.~~450889~~Z",	209	····················"iopub.execute_input":·"2024-05-26T12:10:08.964396Z",
210	····················"iopub.status.busy":·"2024-05-26T09:39:32.450565Z",	210	····················"iopub.status.busy":·"2024-05-26T12:10:08.964076Z",
211	····················"iopub.status.idle":·"2024-05-26T09:39:32.~~574~~429Z",	211	····················"iopub.status.idle":·"2024-05-26T12:10:09.036042Z",
212	····················"shell.execute_reply":·"2024-05-26T09:39:32.~~573603~~Z"	212	····················"shell.execute_reply":·"2024-05-26T12:10:09.035376Z"
213	················}	213	················}
214	············},	214	············},
215	············"outputs":·[	215	············"outputs":·[
216	················{	216	················{
217	····················"name":·"stdout",	217	····················"name":·"stdout",
218	····················"output_type":·"stream",	218	····················"output_type":·"stream",
219	····················"text":·[	219	····················"text":·[
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10	············]	10	············]
11	········},	11	········},
12	········{	12	········{
13	············"cell_type":·"code",	13	············"cell_type":·"code",
14	············"execution_count":·1,	14	············"execution_count":·1,
15	············"metadata":·{	15	············"metadata":·{
16	················"execution":·{	16	················"execution":·{
17	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~4482~~42Z",	17	····················"iopub.execute_input":·"2024-05-26T12:10:03.932648Z",
18	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~447943~~Z",	18	····················"iopub.status.busy":·"2024-05-26T12:10:03.932328Z",
19	····················"iopub.status.idle":·"2024-05-26T09:39:28.~~073997~~Z",	19	····················"iopub.status.idle":·"2024-05-26T12:10:05.380342Z",
20	····················"shell.execute_reply":·"2024-05-26T09:39:28.073073Z"	20	····················"shell.execute_reply":·"2024-05-26T12:10:05.379474Z"
21	················}	21	················}
22	············},	22	············},
23	············"outputs":·[],	23	············"outputs":·[],
24	············"source":·[	24	············"source":·[
25	················"import·numpy·as·np\n",	25	················"import·numpy·as·np\n",
26	················"from·scipy.stats.distributions·import·norm\n",	26	················"from·scipy.stats.distributions·import·norm\n",
27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",	27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",
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61	············]	61	············]
62	········},	62	········},
63	········{	63	········{
64	············"cell_type":·"code",	64	············"cell_type":·"code",
65	············"execution_count":·2,	65	············"execution_count":·2,
66	············"metadata":·{	66	············"metadata":·{
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2024-05-26T09:39:28.08~~7155~~Z",	68	····················"iopub.execute_input":·"2024-05-26T12:10:05.385206Z",
69	····················"iopub.status.busy":·"2024-05-26T09:39:28.086754Z",	69	····················"iopub.status.busy":·"2024-05-26T12:10:05.384749Z",
70	····················"iopub.status.idle":·"2024-05-26T09:39:28.10~~2414~~Z",	70	····················"iopub.status.idle":·"2024-05-26T12:10:05.404278Z",
71	····················"shell.execute_reply":·"2024-05-26T09:39:28.10~~1587~~Z"	71	····················"shell.execute_reply":·"2024-05-26T12:10:05.403459Z"
72	················}	72	················}
73	············},	73	············},
74	············"outputs":·[],	74	············"outputs":·[],
75	············"source":·[	75	············"source":·[
76	················"X·=·np.random.normal(size=(1000,·25))\n",	76	················"X·=·np.random.normal(size=(1000,·25))\n",
77	················"beta·=·np.random.normal(size=25)\n",	77	················"beta·=·np.random.normal(size=25)\n",
78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",	78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",
Offset 88, 18 lines modified		Offset 88, 18 lines modified
88	············]	88	············]
89	········},	89	········},
90	········{	90	········{
91	············"cell_type":·"code",	91	············"cell_type":·"code",
92	············"execution_count":·3,	92	············"execution_count":·3,
93	············"metadata":·{	93	············"metadata":·{
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2024-05-26T09:39:28.108~~981~~Z",	95	····················"iopub.execute_input":·"2024-05-26T12:10:05.408723Z",
96	····················"iopub.status.busy":·"2024-05-26T09:39:28.108~~678~~Z",	96	····················"iopub.status.busy":·"2024-05-26T12:10:05.408407Z",
97	····················"iopub.status.idle":·"2024-05-26T09:39:28.446~~413~~Z",	97	····················"iopub.status.idle":·"2024-05-26T12:10:05.756228Z",
98	····················"shell.execute_reply":·"2024-05-26T09:39:28.445~~631~~Z"	98	····················"shell.execute_reply":·"2024-05-26T12:10:05.755419Z"
99	················}	99	················}
100	············},	100	············},
101	············"outputs":·[],	101	············"outputs":·[],
102	············"source":·[	102	············"source":·[
103	················"debiased_OLS_mod·=·DistributedModel(m)\n",	103	················"debiased_OLS_mod·=·DistributedModel(m)\n",
104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",	104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",
105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",	105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",
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114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·4,	118	············"execution_count":·4,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2024-05-26T09:39:28.~~4547~~09Z",	121	····················"iopub.execute_input":·"2024-05-26T12:10:05.760608Z",
122	····················"iopub.status.busy":·"2024-05-26T09:39:28.~~454399~~Z",	122	····················"iopub.status.busy":·"2024-05-26T12:10:05.760284Z",
123	····················"iopub.status.idle":·"2024-05-26T09:39:29.~~170388~~Z",	123	····················"iopub.status.idle":·"2024-05-26T12:10:06.336295Z",
124	····················"shell.execute_reply":·"2024-05-26T09:39:29.~~169607~~Z"	124	····················"shell.execute_reply":·"2024-05-26T12:10:06.335452Z"
125	················}	125	················}
126	············},	126	············},
127	············"outputs":·[],	127	············"outputs":·[],
128	············"source":·[	128	············"source":·[
129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",	129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",
130	················"from·statsmodels.genmod.families·import·Gaussian\n",	130	················"from·statsmodels.genmod.families·import·Gaussian\n",
131	················"\n",	131	················"\n",
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145	············]	145	············]
146	········},	146	········},
147	········{	147	········{
148	············"cell_type":·"code",	148	············"cell_type":·"code",
149	············"execution_count":·5,	149	············"execution_count":·5,
150	············"metadata":·{	150	············"metadata":·{
151	················"execution":·{	151	················"execution":·{
152	····················"iopub.execute_input":·"2024-05-26T09:39:29.~~178764~~Z",	152	····················"iopub.execute_input":·"2024-05-26T12:10:06.340939Z",
153	····················"iopub.status.busy":·"2024-05-26T09:39:29.~~178454~~Z",	153	····················"iopub.status.busy":·"2024-05-26T12:10:06.340592Z",
154	····················"iopub.status.idle":·"2024-05-26T09:39:29.346~~864~~Z",	154	····················"iopub.status.idle":·"2024-05-26T12:10:06.496245Z",
155	····················"shell.execute_reply":·"2024-05-26T09:39:29.345~~596~~Z"	155	····················"shell.execute_reply":·"2024-05-26T12:10:06.495433Z"
156	················}	156	················}
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",	160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",
161	················"\n",	161	················"\n",
162	················"\n",	162	················"\n",
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176	············]	176	············]
177	········},	177	········},
178	········{	178	········{
179	············"cell_type":·"code",	179	············"cell_type":·"code",
180	············"execution_count":·6,	180	············"execution_count":·6,
181	············"metadata":·{	181	············"metadata":·{
182	················"execution":·{	182	················"execution":·{
183	····················"iopub.execute_input":·"2024-05-26T09:39:29.35~~466~~7Z",	183	····················"iopub.execute_input":·"2024-05-26T12:10:06.500775Z",
184	····················"iopub.status.busy":·"2024-05-26T09:39:29.354376Z",	184	····················"iopub.status.busy":·"2024-05-26T12:10:06.500433Z",
185	····················"iopub.status.idle":·"2024-05-26T09:39:29.382~~363~~Z",	185	····················"iopub.status.idle":·"2024-05-26T12:10:06.532228Z",
186	····················"shell.execute_reply":·"2024-05-26T09:39:29.381~~595~~Z"	186	····················"shell.execute_reply":·"2024-05-26T12:10:06.531417Z"
187	················}	187	················}
188	············},	188	············},
189	············"outputs":·[],	189	············"outputs":·[],
190	············"source":·[	190	············"source":·[
191	················"from·statsmodels.base.distributed_estimation·import·(\n",	191	················"from·statsmodels.base.distributed_estimation·import·(\n",
192	················"····_est_unregularized_naive,\n",	192	················"····_est_unregularized_naive,\n",
193	················"····DistributedResults,\n",	193	················"····DistributedResults,\n",


Offset 468, 14 lines modified		Offset 468, 30 lines modified
468	·N·=············2·····M·=···········10	468	·N·=············2·····M·=···········10

469	At·X0·········0·variables·are·exactly·at·the·bounds	469	At·X0·········0·variables·are·exactly·at·the·bounds

470	At·iterate····0····f=··6.27365D+00····\|proj·g\|=··8.99900D-01	470	At·iterate····0····f=··6.27365D+00····\|proj·g\|=··8.99900D-01

471	At·iterate····1····f=··5.31675D+00····\|proj·g\|=··6.49880D-04	471	At·iterate····1····f=··5.31675D+00····\|proj·g\|=··6.49880D-04
		472	</pre></div></div>
		473	</div>
		474	<div·class="nboutput·docutils·container">
		475	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:
		476	</pre></div>
		477	</div>
		478	<div·class="output_area·docutils·container">
		479	<div·class="highlight"><pre>
		480	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
		481	</pre></div></div>
		482	</div>
		483	<div·class="nboutput·docutils·container">
		484	<div·class="prompt·empty·docutils·container">
		485	</div>
		486	<div·class="output_area·docutils·container">
		487	<div·class="highlight"><pre>

472	At·iterate····2····f=··5.30939D+00····\|proj·g\|=··5.55556D-04	488	At·iterate····2····f=··5.30939D+00····\|proj·g\|=··5.55556D-04

473	At·iterate····3····f=··5.29116D+00····\|proj·g\|=··5.95080D-05	489	At·iterate····3····f=··5.29116D+00····\|proj·g\|=··5.95080D-05

474	At·iterate····4····f=··5.29096D+00····\|proj·g\|=··2.04281D-06	490	At·iterate····4····f=··5.29096D+00····\|proj·g\|=··2.04281D-06

Offset 494, 28 lines modified		Offset 510, 19 lines modified
494	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	510	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
495	····2······4·····13······5·····0·····1···2.043D-06···5.291D+00	511	····2······4·····13······5·····0·····1···2.043D-06···5.291D+00
496	··F·=···5.2909564740670749	512	··F·=···5.2909564740670749

497	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	513	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
498	</pre></div></div>	514	</pre></div></div>
499	</div>	515	</div>
500	<div·class="nboutput·docutils·container">
501	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:
502	</pre></div>
503	</div>
504	<div·class="output_area·docutils·container">
505	<div·class="highlight"><pre>
506	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
507	</pre></div></div>
508	</div>
509	<div·class="nboutput·nblast·docutils·container">	516	<div·class="nboutput·nblast·docutils·container">
510	<div·class="prompt·empty·docutils·container">	517	<div·class="prompt·empty·docutils·container">
511	</div>	518	</div>
512	<div·class="output_area·docutils·container">	519	<div·class="output_area·docutils·container">
513	<img·alt="../../../_images/examples_notebooks_generated_ets_6_2.png"·src="../../../_images/examples_notebooks_generated_ets_6_2.png"·/>	520	<img·alt="../../../_images/examples_notebooks_generated_ets_6_3.png"·src="../../../_images/examples_notebooks_generated_ets_6_3.png"·/>
514	</div>	521	</div>
515	</div>	522	</div>
516	<p>By·default·the·initial·states·are·considered·to·be·fitting·parameters·and·are·estimated·by·maximizing·log-likelihood.·It·is·possible·to·only·use·a·heuristic·for·the·initial·values:</p>	523	<p>By·default·the·initial·states·are·considered·to·be·fitting·parameters·and·are·estimated·by·maximizing·log-likelihood.·It·is·possible·to·only·use·a·heuristic·for·the·initial·values:</p>
517	<div·class="nbinput·docutils·container">	524	<div·class="nbinput·docutils·container">
518	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:	525	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:
519	</pre></div>	526	</pre></div>
520	</div>	527	</div>
Offset 532, 14 lines modified		Offset 539, 23 lines modified
532	<span·class="n">yhat</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"with·R·params"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">":"</span><span·class="p">)</span>	539	<span·class="n">yhat</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"with·R·params"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">":"</span><span·class="p">)</span>

533	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>	540	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>
534	</pre></div>	541	</pre></div>
535	</div>	542	</div>
536	</div>	543	</div>
537	<div·class="nboutput·docutils·container">	544	<div·class="nboutput·docutils·container">
		545	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:
		546	</pre></div>
		547	</div>
		548	<div·class="output_area·docutils·container">
		549	<div·class="highlight"><pre>
		550	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
		551	</pre></div></div>
		552	</div>
		553	<div·class="nboutput·docutils·container">
538	<div·class="prompt·empty·docutils·container">	554	<div·class="prompt·empty·docutils·container">
539	</div>	555	</div>
540	<div·class="output_area·docutils·container">	556	<div·class="output_area·docutils·container">
541	<div·class="highlight"><pre>	557	<div·class="highlight"><pre>
542	RUNNING·THE·L-BFGS-B·CODE	558	RUNNING·THE·L-BFGS-B·CODE

543	·············*	559	·············*
Offset 568, 23 lines modified		Offset 584, 14 lines modified
568	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	584	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
569	····1······1······2······1·····0·····1···0.000D+00···5.317D+00	585	····1······1······2······1·····0·····1···0.000D+00···5.317D+00
570	··F·=···5.3167544390512402	586	··F·=···5.3167544390512402

571	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	587	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
572	</pre></div></div>	588	</pre></div></div>
573	</div>	589	</div>
574	<div·class="nboutput·docutils·container">
575	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:
576	</pre></div>
577	</div>
578	<div·class="output_area·docutils·container">
579	<div·class="highlight"><pre>
580	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
581	</pre></div></div>
582	</div>
583	<div·class="nboutput·nblast·docutils·container">	590	<div·class="nboutput·nblast·docutils·container">
584	<div·class="prompt·empty·docutils·container">	591	<div·class="prompt·empty·docutils·container">
585	</div>	592	</div>
586	<div·class="output_area·docutils·container">	593	<div·class="output_area·docutils·container">
587	<img·alt="../../../_images/examples_notebooks_generated_ets_8_2.png"·src="../../../_images/examples_notebooks_generated_ets_8_2.png"·/>	594	<img·alt="../../../_images/examples_notebooks_generated_ets_8_2.png"·src="../../../_images/examples_notebooks_generated_ets_8_2.png"·/>
588	</div>	595	</div>
589	</div>	596	</div>
Offset 811, 14 lines modified		Offset 818, 23 lines modified
811	<span·class="n">fit</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"statsmodels·fit"</span><span·class="p">)</span>	818	<span·class="n">fit</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"statsmodels·fit"</span><span·class="p">)</span>
812	<span·class="n">fit_R</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"R·fit"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">"--"</span><span·class="p">)</span>	819	<span·class="n">fit_R</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">label</span><span·class="o">=</span><span·class="s2">"R·fit"</span><span·class="p">,</span>·<span·class="n">linestyle</span><span·class="o">=</span><span·class="s2">"--"</span><span·class="p">)</span>
813	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>	820	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>
814	</pre></div>	821	</pre></div>
815	</div>	822	</div>
816	</div>	823	</div>
817	<div·class="nboutput·docutils·container">	824	<div·class="nboutput·docutils·container">
		825	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:
		826	</pre></div>
		827	</div>
		828	<div·class="output_area·docutils·container">
		829	<div·class="highlight"><pre>
		830	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
		831	</pre></div></div>
		832	</div>
		833	<div·class="nboutput·docutils·container">
818	<div·class="prompt·empty·docutils·container">	834	<div·class="prompt·empty·docutils·container">
819	</div>	835	</div>
820	<div·class="output_area·docutils·container">	836	<div·class="output_area·docutils·container">
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Offset 131, 14 lines modified		Offset 131, 16 lines modified
131	·N·=············2·····M·=···········10	131	·N·=············2·····M·=···········10

132	At·X0·········0·variables·are·exactly·at·the·bounds	132	At·X0·········0·variables·are·exactly·at·the·bounds

133	At·iterate····0····f=··6.27365D+00····\|proj·g\|=··8.99900D-01	133	At·iterate····0····f=··6.27365D+00····\|proj·g\|=··8.99900D-01

134	At·iterate····1····f=··5.31675D+00····\|proj·g\|=··6.49880D-04	134	At·iterate····1····f=··5.31675D+00····\|proj·g\|=··6.49880D-04
		135	[4]:
		136	<matplotlib.legend.Legend·at·0xadde5de1e8ed>

135	At·iterate····2····f=··5.30939D+00····\|proj·g\|=··5.55556D-04	137	At·iterate····2····f=··5.30939D+00····\|proj·g\|=··5.55556D-04

136	At·iterate····3····f=··5.29116D+00····\|proj·g\|=··5.95080D-05	138	At·iterate····3····f=··5.29116D+00····\|proj·g\|=··5.95080D-05

137	At·iterate····4····f=··5.29096D+00····\|proj·g\|=··2.04281D-06	139	At·iterate····4····f=··5.29096D+00····\|proj·g\|=··2.04281D-06

Offset 155, 17 lines modified		Offset 157, 15 lines modified
155	·············*	157	·············*

156	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	158	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
157	····2······4·····13······5·····0·····1···2.043D-06···5.291D+00	159	····2······4·····13······5·····0·····1···2.043D-06···5.291D+00
158	··F·=···5.2909564740670749	160	··F·=···5.2909564740670749

159	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	161	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
160	[4]:
161	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
162	[../../../_images/examples_notebooks_generated_ets_6_2.png]	162	[../../../_images/examples_notebooks_generated_ets_6_3.png]
163	By·default·the·initial·states·are·considered·to·be·fitting·parameters·and·are	163	By·default·the·initial·states·are·considered·to·be·fitting·parameters·and·are
164	estimated·by·maximizing·log-likelihood.·It·is·possible·to·only·use·a·heuristic	164	estimated·by·maximizing·log-likelihood.·It·is·possible·to·only·use·a·heuristic
165	for·the·initial·values:	165	for·the·initial·values:
166	[5]:	166	[5]:
167	model_heuristic·=·ETSModel(oil,·initialization_method="heuristic")	167	model_heuristic·=·ETSModel(oil,·initialization_method="heuristic")
168	fit_heuristic·=·model_heuristic.fit()	168	fit_heuristic·=·model_heuristic.fit()
169	oil.plot(label="data")	169	oil.plot(label="data")
Offset 176, 14 lines modified		Offset 176, 16 lines modified
176	#·obtained·from·R	176	#·obtained·from·R
177	params·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,	177	params·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,
178	34.72584983]	178	34.72584983]
179	yhat·=·model.smooth(params).fittedvalues	179	yhat·=·model.smooth(params).fittedvalues
180	yhat.plot(label="with·R·params",·linestyle=":")	180	yhat.plot(label="with·R·params",·linestyle=":")

181	plt.legend()	181	plt.legend()
		182	[5]:
		183	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
182	RUNNING·THE·L-BFGS-B·CODE	184	RUNNING·THE·L-BFGS-B·CODE

183	·············*	185	·············*

184	Machine·precision·=·2.220D-16	186	Machine·precision·=·2.220D-16
185	·N·=············1·····M·=···········10	187	·N·=············1·····M·=···········10

Offset 206, 16 lines modified		Offset 208, 14 lines modified
206	·············*	208	·············*

207	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	209	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
208	····1······1······2······1·····0·····1···0.000D+00···5.317D+00	210	····1······1······2······1·····0·····1···0.000D+00···5.317D+00
209	··F·=···5.3167544390512402	211	··F·=···5.3167544390512402

210	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	212	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
211	[5]:
212	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
213	[../../../_images/examples_notebooks_generated_ets_8_2.png]	213	[../../../_images/examples_notebooks_generated_ets_8_2.png]
214	The·fitted·parameters·and·some·other·measures·are·shown·using·fit.summary().	214	The·fitted·parameters·and·some·other·measures·are·shown·using·fit.summary().
215	Here·we·can·see·that·the·log-likelihood·of·the·model·using·fitted·initial	215	Here·we·can·see·that·the·log-likelihood·of·the·model·using·fitted·initial
216	states·is·fractionally·lower·than·the·one·using·a·heuristic·for·the·initial	216	states·is·fractionally·lower·than·the·one·using·a·heuristic·for·the·initial
217	states.	217	states.
218	[6]:	218	[6]:
219	print(fit.summary())	219	print(fit.summary())
Offset 402, 14 lines modified		Offset 402, 16 lines modified

402	austourists.plot(label="data")	402	austourists.plot(label="data")
403	plt.ylabel("Australian·Tourists")	403	plt.ylabel("Australian·Tourists")

404	fit.fittedvalues.plot(label="statsmodels·fit")	404	fit.fittedvalues.plot(label="statsmodels·fit")
405	fit_R.fittedvalues.plot(label="R·fit",·linestyle="--")	405	fit_R.fittedvalues.plot(label="R·fit",·linestyle="--")
406	plt.legend()	406	plt.legend()
		407	[9]:
		408	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
407	RUNNING·THE·L-BFGS-B·CODE	409	RUNNING·THE·L-BFGS-B·CODE

408	·············*	410	·············*

409	Machine·precision·=·2.220D-16	411	Machine·precision·=·2.220D-16
410	·N·=············9·····M·=···········10	412	·N·=············9·····M·=···········10

Offset 596, 16 lines modified		Offset 598, 14 lines modified
596	·············*	598	·············*

597	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	599	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
598	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00	600	····9·····82····102·····90·····0·····1···1.643D-05···2.245D+00
599	··F·=···2.2445124982934956	601	··F·=···2.2445124982934956

600	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH	602	CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
601	[9]:
602	<matplotlib.legend.Legend·at·0xadde5de1e8ed>
603	[../../../_images/examples_notebooks_generated_ets_14_2.png]	603	[../../../_images/examples_notebooks_generated_ets_14_2.png]
604	[10]:	604	[10]:
605	print(fit.summary())	605	print(fit.summary())
606	·································ETS·Results	606	·································ETS·Results
607	==============================================================================	607	==============================================================================
608	Dep.·Variable:······················y···No.·Observations:···················68	608	Dep.·Variable:······················y···No.·Observations:···················68
609	Model:······················ETS(AAdA)···Log·Likelihood················-152.627	609	Model:······················ETS(AAdA)···Log·Likelihood················-152.627


Offset 486, 27 lines modified		Offset 486, 27 lines modified
486	······<th></th>	486	······<th></th>
487	······<th>Variance</th>	487	······<th>Variance</th>
488	····</tr>	488	····</tr>
489	··</thead>	489	··</thead>
490	··<tbody>	490	··<tbody>
491	····<tr>	491	····<tr>
492	······<th>groups_ix</th>	492	······<th>groups_ix</th>
493	······<td>1.133164</td>	493	······<td>1.043924</td>
494	····</tr>	494	····</tr>
495	····<tr>	495	····<tr>
496	······<th>level1_ix</th>	496	······<th>level1_ix</th>
497	······<td>1.~~957912~~</td>	497	······<td>1.868659</td>
498	····</tr>	498	····</tr>
499	····<tr>	499	····<tr>
500	······<th>level2_ix</th>	500	······<th>level2_ix</th>
501	······<td>2.9~~36815~~</td>	501	······<td>2.984989</td>
502	····</tr>	502	····</tr>
503	····<tr>	503	····<tr>
504	······<th>Residual</th>	504	······<th>Residual</th>
505	······<td>4.~~0393~~57</td>	505	······<td>3.986159</td>
506	····</tr>	506	····</tr>
507	··</tbody>	507	··</tbody>
508	</table>	508	</table>
509	</div></div>	509	</div></div>
510	</div>	510	</div>
511	</section>	511	</section>


Offset 79, 18 lines modified		Offset 79, 18 lines modified
79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,	79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,
80	level1_var,·etc.·as·defined·above.	80	level1_var,·etc.·as·defined·above.
81	[13]:	81	[13]:
82	r.cov_struct.summary()	82	r.cov_struct.summary()
83	[13]:	83	[13]:
84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·	84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·
85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|	85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|
86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_\x8._\x81_.3_.3_.1_.6_\x84\|	86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_\x8._\x80_.4_.3_.9_.2_\x84\|
87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_\x8._\x89_.5_.7_.9_.1_.2\|	87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_\x8._\x88_.6_.8_.6_.5_.9\|
88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x89_\x83_.6_.8_.1_.5\|	88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x89_\x88_.4_.9_.8_.9\|
89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x84_.._.0_.3_.9_.3_.5_.7\|	89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x83_.._.9_.8_.6_.1_.5_.9\|
90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8]	90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8]
91	\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	91	\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
92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s	92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d	93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
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47	····················"shell.execute_reply":·"2024-05-26T09:39:26.929605Z"	47	····················"shell.execute_reply":·"2024-05-26T12:10:04.359375Z"
48	················}	48	················}
49	············},	49	············},
50	············"outputs":·[],	50	············"outputs":·[],
51	············"source":·[	51	············"source":·[
52	················"p·=·5"	52	················"p·=·5"
53	············]	53	············]
54	········},	54	········},
Offset 60, 18 lines modified		Offset 60, 18 lines modified
60	············]	60	············]
61	········},	61	········},
62	········{	62	········{
63	············"cell_type":·"code",	63	············"cell_type":·"code",
64	············"execution_count":·3,	64	············"execution_count":·3,
65	············"metadata":·{	65	············"metadata":·{
66	················"execution":·{	66	················"execution":·{
67	····················"iopub.execute_input":·"2024-05-26T09:39:26.938~~689~~Z",	67	····················"iopub.execute_input":·"2024-05-26T12:10:04.368462Z",
68	····················"iopub.status.busy":·"2024-05-26T09:39:26.938~~394~~Z",	68	····················"iopub.status.busy":·"2024-05-26T12:10:04.368137Z",
69	····················"iopub.status.idle":·"2024-05-26T09:39:26.946~~569~~Z",	69	····················"iopub.status.idle":·"2024-05-26T12:10:04.376057Z",
70	····················"shell.execute_reply":·"2024-05-26T09:39:26.945776Z"	70	····················"shell.execute_reply":·"2024-05-26T12:10:04.375376Z"
71	················}	71	················}
72	············},	72	············},
73	············"outputs":·[],	73	············"outputs":·[],
74	············"source":·[	74	············"source":·[
75	················"groups_var·=·1\n",	75	················"groups_var·=·1\n",
76	················"level1_var·=·2\n",	76	················"level1_var·=·2\n",
77	················"level2_var·=·3\n",	77	················"level2_var·=·3\n",
Offset 86, 18 lines modified		Offset 86, 18 lines modified
86	············]	86	············]
87	········},	87	········},
88	········{	88	········{
89	············"cell_type":·"code",	89	············"cell_type":·"code",
90	············"execution_count":·4,	90	············"execution_count":·4,
91	············"metadata":·{	91	············"metadata":·{
92	················"execution":·{	92	················"execution":·{
93	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~95030~~7Z",	93	····················"iopub.execute_input":·"2024-05-26T12:10:04.384457Z",
94	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~950012~~Z",	94	····················"iopub.status.busy":·"2024-05-26T12:10:04.384137Z",
95	····················"iopub.status.idle":·"2024-05-26T09:39:26.958~~381~~Z",	95	····················"iopub.status.idle":·"2024-05-26T12:10:04.395573Z",
96	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~957594~~Z"	96	····················"shell.execute_reply":·"2024-05-26T12:10:04.388186Z"
97	················}	97	················}
98	············},	98	············},
99	············"outputs":·[],	99	············"outputs":·[],
100	············"source":·[	100	············"source":·[
101	················"n_groups·=·100"	101	················"n_groups·=·100"
102	············]	102	············]
103	········},	103	········},
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109	············]	109	············]
110	········},	110	········},
111	········{	111	········{
112	············"cell_type":·"code",	112	············"cell_type":·"code",
113	············"execution_count":·5,	113	············"execution_count":·5,
114	············"metadata":·{	114	············"metadata":·{
115	················"execution":·{	115	················"execution":·{
116	····················"iopub.execute_input":·"2024-05-26T09:39:26.962184Z",	116	····················"iopub.execute_input":·"2024-05-26T12:10:04.402580Z",
117	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~961854~~Z",	117	····················"iopub.status.busy":·"2024-05-26T12:10:04.402263Z",
118	····················"iopub.status.idle":·"2024-05-26T09:39:26.~~970434~~Z",	118	····················"iopub.status.idle":·"2024-05-26T12:10:04.412140Z",
119	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~969635~~Z"	119	····················"shell.execute_reply":·"2024-05-26T12:10:04.411402Z"
120	················}	120	················}
121	············},	121	············},
122	············"outputs":·[],	122	············"outputs":·[],
123	············"source":·[	123	············"source":·[
124	················"group_size·=·20\n",	124	················"group_size·=·20\n",
125	················"level1_size·=·10\n",	125	················"level1_size·=·10\n",
126	················"level2_size·=·5"	126	················"level2_size·=·5"
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134	············]	134	············]
135	········},	135	········},
136	········{	136	········{
137	············"cell_type":·"code",	137	············"cell_type":·"code",
138	············"execution_count":·6,	138	············"execution_count":·6,
139	············"metadata":·{	139	············"metadata":·{
140	················"execution":·{	140	················"execution":·{
141	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~974144~~Z",	141	····················"iopub.execute_input":·"2024-05-26T12:10:04.416301Z",
142	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~973826~~Z",	142	····················"iopub.status.busy":·"2024-05-26T12:10:04.415994Z",
143	····················"iopub.status.idle":·"2024-05-26T09:39:26.~~982369~~Z",	143	····················"iopub.status.idle":·"2024-05-26T12:10:04.424152Z",
144	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~981589~~Z"	144	····················"shell.execute_reply":·"2024-05-26T12:10:04.423405Z"
145	················}	145	················}
146	············},	146	············},
147	············"outputs":·[],	147	············"outputs":·[],
148	············"source":·[	148	············"source":·[
149	················"n·=·n_groups··group_size··level1_size·*·level2_size"	149	················"n·=·n_groups··group_size··level1_size·*·level2_size"
150	············]	150	············]
151	········},	151	········},
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157	············]	157	············]
158	········},	158	········},
159	········{	159	········{
160	············"cell_type":·"code",	160	············"cell_type":·"code",
161	············"execution_count":·7,	161	············"execution_count":·7,
162	············"metadata":·{	162	············"metadata":·{
163	················"execution":·{	163	················"execution":·{
164	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~98636~~9Z",	164	····················"iopub.execute_input":·"2024-05-26T12:10:04.428449Z",
165	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~986080~~Z",	165	····················"iopub.status.busy":·"2024-05-26T12:10:04.428121Z",
166	····················"iopub.status.idle":·"2024-05-26T09:39:27.~~026450~~Z",	166	····················"iopub.status.idle":·"2024-05-26T12:10:04.468176Z",
167	····················"shell.execute_reply":·"2024-05-26T09:39:27.~~0256~~42Z"	167	····················"shell.execute_reply":·"2024-05-26T12:10:04.467449Z"
168	················}	168	················}
169	············},	169	············},
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14	············]	14	············]
15	········},	15	········},
16	········{	16	········{
17	············"cell_type":·"code",	17	············"cell_type":·"code",
18	············"execution_count":·1,	18	············"execution_count":·1,
19	············"metadata":·{	19	············"metadata":·{
20	················"execution":·{	20	················"execution":·{
21	····················"iopub.execute_input":·"2024-05-26T09:38:04.338160Z",	21	····················"iopub.execute_input":·"2024-05-26T12:08:55.873809Z",
22	····················"iopub.status.busy":·"2024-05-26T09:38:04.~~337472~~Z",	22	····················"iopub.status.busy":·"2024-05-26T12:08:55.873338Z",
23	····················"iopub.status.idle":·"2024-05-26T09:38:06.~~878409~~Z",	23	····················"iopub.status.idle":·"2024-05-26T12:08:58.312267Z",
24	····················"shell.execute_reply":·"2024-05-26T09:38:06.~~877598~~Z"	24	····················"shell.execute_reply":·"2024-05-26T12:08:58.311429Z"
25	················}	25	················}
26	············},	26	············},
27	············"outputs":·[],	27	············"outputs":·[],
28	············"source":·[	28	············"source":·[
29	················"import·pandas·as·pd\n",	29	················"import·pandas·as·pd\n",
30	················"import·numpy·as·np\n",	30	················"import·numpy·as·np\n",
31	················"from·scipy.stats.distributions·import·norm,·poisson\n",	31	················"from·scipy.stats.distributions·import·norm,·poisson\n",
Offset 42, 18 lines modified		Offset 42, 18 lines modified
42	············]	42	············]
43	········},	43	········},
44	········{	44	········{
45	············"cell_type":·"code",	45	············"cell_type":·"code",
46	············"execution_count":·2,	46	············"execution_count":·2,
47	············"metadata":·{	47	············"metadata":·{
48	················"execution":·{	48	················"execution":·{
49	····················"iopub.execute_input":·"2024-05-26T09:38:06.~~886844~~Z",	49	····················"iopub.execute_input":·"2024-05-26T12:08:58.320737Z",
50	····················"iopub.status.busy":·"2024-05-26T09:38:06.~~886414~~Z",	50	····················"iopub.status.busy":·"2024-05-26T12:08:58.320267Z",
51	····················"iopub.status.idle":·"2024-05-26T09:38:06.~~8983~~94Z",	51	····················"iopub.status.idle":·"2024-05-26T12:08:58.332193Z",
52	····················"shell.execute_reply":·"2024-05-26T09:38:06.~~897638~~Z"	52	····················"shell.execute_reply":·"2024-05-26T12:08:58.331415Z"
53	················},	53	················},
54	················"lines_to_next_cell":·1	54	················"lines_to_next_cell":·1
55	············},	55	············},
56	············"outputs":·[],	56	············"outputs":·[],
57	············"source":·[	57	············"source":·[
58	················"def·negbinom(u,·mu,·scale):\n",	58	················"def·negbinom(u,·mu,·scale):\n",
59	················"····p·=·(scale·-·1)·/·scale\n",	59	················"····p·=·(scale·-·1)·/·scale\n",
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70	············]	70	············]
71	········},	71	········},
72	········{	72	········{
73	············"cell_type":·"code",	73	············"cell_type":·"code",
74	············"execution_count":·3,	74	············"execution_count":·3,
75	············"metadata":·{	75	············"metadata":·{
76	················"execution":·{	76	················"execution":·{
77	····················"iopub.execute_input":·"2024-05-26T09:38:06.~~902329~~Z",	77	····················"iopub.execute_input":·"2024-05-26T12:08:58.340546Z",
78	····················"iopub.status.busy":·"2024-05-26T09:38:06.902027Z",	78	····················"iopub.status.busy":·"2024-05-26T12:08:58.340230Z",
79	····················"iopub.status.idle":·"2024-05-26T09:38:06.~~91036~~6Z",	79	····················"iopub.status.idle":·"2024-05-26T12:08:58.352246Z",
80	····················"shell.execute_reply":·"2024-05-26T09:38:06.~~909584~~Z"	80	····················"shell.execute_reply":·"2024-05-26T12:08:58.351463Z"
81	················}	81	················}
82	············},	82	············},
83	············"outputs":·[],	83	············"outputs":·[],
84	············"source":·[	84	············"source":·[
85	················"#·Sample·size\n",	85	················"#·Sample·size\n",
86	················"n·=·1000\n",	86	················"n·=·1000\n",
87	················"\n",	87	················"\n",
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106	············]	106	············]
107	········},	107	········},
108	········{	108	········{
109	············"cell_type":·"code",	109	············"cell_type":·"code",
110	············"execution_count":·4,	110	············"execution_count":·4,
111	············"metadata":·{	111	············"metadata":·{
112	················"execution":·{	112	················"execution":·{
113	····················"iopub.execute_input":·"2024-05-26T09:38:06.~~914473~~Z",	113	····················"iopub.execute_input":·"2024-05-26T12:08:58.360515Z",
114	····················"iopub.status.busy":·"2024-05-26T09:38:06.~~914173~~Z",	114	····················"iopub.status.busy":·"2024-05-26T12:08:58.360208Z",
115	····················"iopub.status.idle":·"2024-05-26T09:38:06.~~930397~~Z",	115	····················"iopub.status.idle":·"2024-05-26T12:08:58.368258Z",
116	····················"shell.execute_reply":·"2024-05-26T09:38:06.~~92960~~1Z"	116	····················"shell.execute_reply":·"2024-05-26T12:08:58.367431Z"
117	················}	117	················}
118	············},	118	············},
119	············"outputs":·[],	119	············"outputs":·[],
120	············"source":·[	120	············"source":·[
121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",	121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",
122	················"x·=·np.random.normal(size=(n,·p))\n",	122	················"x·=·np.random.normal(size=(n,·p))\n",
123	················"x[:,·0]·=·1"	123	················"x[:,·0]·=·1"
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131	············]	131	············]
132	········},	132	········},
133	········{	133	········{
134	············"cell_type":·"code",	134	············"cell_type":·"code",
135	············"execution_count":·5,	135	············"execution_count":·5,
136	············"metadata":·{	136	············"metadata":·{
137	················"execution":·{	137	················"execution":·{
138	····················"iopub.execute_input":·"2024-05-26T09:38:06.~~934285~~Z",	138	····················"iopub.execute_input":·"2024-05-26T12:08:58.376567Z",
139	····················"iopub.status.busy":·"2024-05-26T09:38:06.~~933991~~Z",	139	····················"iopub.status.busy":·"2024-05-26T12:08:58.376254Z",
140	····················"iopub.status.idle":·"2024-05-26T09:38:06.~~942~~353Z",	140	····················"iopub.status.idle":·"2024-05-26T12:08:58.384305Z",
141	····················"shell.execute_reply":·"2024-05-26T09:38:06.~~941590~~Z"	141	····················"shell.execute_reply":·"2024-05-26T12:08:58.383442Z"
142	················}	142	················}
143	············},	143	············},
144	············"outputs":·[],	144	············"outputs":·[],
145	············"source":·[	145	············"source":·[
146	················"x0·=·x[:,·0:3]"	146	················"x0·=·x[:,·0:3]"
147	············]	147	············]
148	········},	148	········},
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154	············]	154	············]
155	········},	155	········},
156	········{	156	········{
157	············"cell_type":·"code",	157	············"cell_type":·"code",
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39	················"import·numpy·as·np\n",	39	················"import·numpy·as·np\n",
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66	····················"iopub.execute_input":·"2024-05-26T09:39:26.507086Z",	66	····················"iopub.execute_input":·"2024-05-26T12:10:02.720841Z",
67	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~506628~~Z",	67	····················"iopub.status.busy":·"2024-05-26T12:10:02.720351Z",
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69	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~51760~~0Z"	69	····················"shell.execute_reply":·"2024-05-26T12:10:02.731440Z"
70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
74	····················"name":·"stdout",	74	····················"name":·"stdout",
75	····················"output_type":·"stream",	75	····················"output_type":·"stream",
76	····················"text":·[	76	····················"text":·[
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128	············]	128	············]
129	········},	129	········},
130	········{	130	········{
131	············"cell_type":·"code",	131	············"cell_type":·"code",
132	············"execution_count":·4,	132	············"execution_count":·4,
133	············"metadata":·{	133	············"metadata":·{
134	················"execution":·{	134	················"execution":·{
135	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~522342~~Z",	135	····················"iopub.execute_input":·"2024-05-26T12:10:02.740604Z",
136	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~522005~~Z",	136	····················"iopub.status.busy":·"2024-05-26T12:10:02.740262Z",
137	····················"iopub.status.idle":·"2024-05-26T09:39:26.~~55846~~0Z",	137	····················"iopub.status.idle":·"2024-05-26T12:10:02.780200Z",
138	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~55760~~6Z"	138	····················"shell.execute_reply":·"2024-05-26T12:10:02.779416Z"
139	················}	139	················}
140	············},	140	············},
141	············"outputs":·[],	141	············"outputs":·[],
142	············"source":·[	142	············"source":·[
143	················"data·=·sm.datasets.star98.load()\n",	143	················"data·=·sm.datasets.star98.load()\n",
144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"	144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"
145	············]	145	············]
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152	············]	152	············]
153	········},	153	········},
154	········{	154	········{
155	············"cell_type":·"code",	155	············"cell_type":·"code",
156	············"execution_count":·5,	156	············"execution_count":·5,
157	············"metadata":·{	157	············"metadata":·{
158	················"execution":·{	158	················"execution":·{
159	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~5628~~94Z",	159	····················"iopub.execute_input":·"2024-05-26T12:10:02.784796Z",
160	····················"iopub.status.busy":·"2024-05-26T09:39:26.~~562576~~Z",	160	····················"iopub.status.busy":·"2024-05-26T12:10:02.784458Z",
161	····················"iopub.status.idle":·"2024-05-26T09:39:26.~~578441~~Z",	161	····················"iopub.status.idle":·"2024-05-26T12:10:02.800217Z",
162	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~577605~~Z"	162	····················"shell.execute_reply":·"2024-05-26T12:10:02.799431Z"
163	················}	163	················}
164	············},	164	············},
165	············"outputs":·[	165	············"outputs":·[
166	················{	166	················{
167	····················"name":·"stdout",	167	····················"name":·"stdout",
168	····················"output_type":·"stream",	168	····················"output_type":·"stream",
169	····················"text":·[	169	····················"text":·[
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189	············]	189	············]
190	········},	190	········},
191	········{	191	········{
192	············"cell_type":·"code",	192	············"cell_type":·"code",
193	············"execution_count":·6,	193	············"execution_count":·6,
194	············"metadata":·{	194	············"metadata":·{
195	················"execution":·{	195	················"execution":·{
196	····················"iopub.execute_input":·"2024-05-26T09:39:26.~~582337~~Z",	196	····················"iopub.execute_input":·"2024-05-26T12:10:02.804625Z",
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198	····················"iopub.status.idle":·"2024-05-26T09:39:26.610~~441~~Z",	198	····················"iopub.status.idle":·"2024-05-26T12:10:02.840175Z",
199	····················"shell.execute_reply":·"2024-05-26T09:39:26.609621Z"	199	····················"shell.execute_reply":·"2024-05-26T12:10:02.839411Z"
200	················}	200	················}
201	············},	201	············},
202	············"outputs":·[	202	············"outputs":·[
203	················{	203	················{
204	····················"name":·"stdout",	204	····················"name":·"stdout",
205	····················"output_type":·"stream",	205	····················"output_type":·"stream",
206	····················"text":·[	206	····················"text":·[
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248	············]	248	············]
249	········},	249	········},
250	········{	250	········{
251	············"cell_type":·"code",	251	············"cell_type":·"code",
252	············"execution_count":·7,	252	············"execution_count":·7,
253	············"metadata":·{	253	············"metadata":·{
254	················"execution":·{	254	················"execution":·{
255	····················"iopub.execute_input":·"2024-05-26T09:39:26.614~~745~~Z",	255	····················"iopub.execute_input":·"2024-05-26T12:10:02.844473Z",
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258	····················"shell.execute_reply":·"2024-05-26T09:39:26.~~64158~~9Z"	258	····················"shell.execute_reply":·"2024-05-26T12:10:02.887429Z"
259	················}	259	················}
260	············},	260	············},
261	············"outputs":·[	261	············"outputs":·[
262	················{	262	················{
263	····················"name":·"stdout",	263	····················"name":·"stdout",
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Offset 486, 17 lines modified		Offset 486, 17 lines modified
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_2~~477353~~/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_158670/1000445862.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_2~~477353~~/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_158670/1000445862.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>


Offset 176, 20 lines modified		Offset 176, 20 lines modified
176	As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half	176	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	-0.020395987154756403	181	-0.020395987154756403
182	-0.020395987154757343	182	-0.020395987154757343
183	/tmp/ipykernel_2~~477353~~/1000445862.py:1:·FutureWarning:·Series.__getitem__	183	/tmp/ipykernel_158670/1000445862.py:1:·FutureWarning:·Series.__getitem__
184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
185	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	185	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_2~~477353~~/1000445862.py:2:·FutureWarning:·Series.__getitem__	188	/tmp/ipykernel_158670/1000445862.py:2:·FutureWarning:·Series.__getitem__
189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
190	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	190	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_\x8s	195	····*·_\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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17	············]	17	············]
18	········},	18	········},
19	········{	19	········{
20	············"cell_type":·"code",	20	············"cell_type":·"code",
21	············"execution_count":·1,	21	············"execution_count":·1,
22	············"metadata":·{	22	············"metadata":·{
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24	····················"iopub.execute_input":·"2024-05-26T09:39:21.289701Z",	24	····················"iopub.execute_input":·"2024-05-26T12:09:59.628206Z",
25	····················"iopub.status.busy":·"2024-05-26T09:39:21.~~28936~~9Z",	25	····················"iopub.status.busy":·"2024-05-26T12:09:59.627879Z",
26	····················"iopub.status.idle":·"2024-05-26T09:39:23.494488Z",	26	····················"iopub.status.idle":·"2024-05-26T12:10:01.844281Z",
27	····················"shell.execute_reply":·"2024-05-26T09:39:23.493~~623~~Z"	27	····················"shell.execute_reply":·"2024-05-26T12:10:01.843449Z"
28	················},	28	················},
29	················"jupyter":·{	29	················"jupyter":·{
30	····················"outputs_hidden":·false	30	····················"outputs_hidden":·false
31	················}	31	················}
32	············},	32	············},
33	············"outputs":·[],	33	············"outputs":·[],
34	············"source":·[	34	············"source":·[
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69	············]	69	············]
70	········},	70	········},
71	········{	71	········{
72	············"cell_type":·"code",	72	············"cell_type":·"code",
73	············"execution_count":·2,	73	············"execution_count":·2,
74	············"metadata":·{	74	············"metadata":·{
75	················"execution":·{	75	················"execution":·{
76	····················"iopub.execute_input":·"2024-05-26T09:39:23.~~50279~~6Z",	76	····················"iopub.execute_input":·"2024-05-26T12:10:01.864676Z",
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78	····················"iopub.status.idle":·"2024-05-26T09:39:23.59~~843~~0Z",	78	····················"iopub.status.idle":·"2024-05-26T12:10:01.910202Z",
79	····················"shell.execute_reply":·"2024-05-26T09:39:23.~~597602~~Z"	79	····················"shell.execute_reply":·"2024-05-26T12:10:01.909386Z"
80	················},	80	················},
81	················"jupyter":·{	81	················"jupyter":·{
82	····················"outputs_hidden":·false	82	····················"outputs_hidden":·false
83	················}	83	················}
84	············},	84	············},
85	············"outputs":·[	85	············"outputs":·[
86	················{	86	················{
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139	············]	139	············]
140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
143	············"execution_count":·3,	143	············"execution_count":·3,
144	············"metadata":·{	144	············"metadata":·{
145	················"execution":·{	145	················"execution":·{
146	····················"iopub.execute_input":·"2024-05-26T09:39:23.~~602773~~Z",	146	····················"iopub.execute_input":·"2024-05-26T12:10:01.914388Z",
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148	····················"iopub.status.idle":·"2024-05-26T09:39:23.698398Z",	148	····················"iopub.status.idle":·"2024-05-26T12:10:01.975809Z",
149	····················"shell.execute_reply":·"2024-05-26T09:39:23.697~~587~~Z"	149	····················"shell.execute_reply":·"2024-05-26T12:10:01.967454Z"
150	················},	150	················},
151	················"jupyter":·{	151	················"jupyter":·{
152	····················"outputs_hidden":·false	152	····················"outputs_hidden":·false
153	················}	153	················}
154	············},	154	············},
155	············"outputs":·[	155	············"outputs":·[
156	················{	156	················{
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215	············]	215	············]
216	········},	216	········},
217	········{	217	········{
218	············"cell_type":·"code",	218	············"cell_type":·"code",
219	············"execution_count":·4,	219	············"execution_count":·4,
220	············"metadata":·{	220	············"metadata":·{
221	················"execution":·{	221	················"execution":·{
222	····················"iopub.execute_input":·"2024-05-26T09:39:23.~~7029~~22Z",	222	····················"iopub.execute_input":·"2024-05-26T12:10:01.980321Z",
223	····················"iopub.status.busy":·"2024-05-26T09:39:23.~~702591~~Z",	223	····················"iopub.status.busy":·"2024-05-26T12:10:01.980005Z",
224	····················"iopub.status.idle":·"2024-05-26T09:39:23.~~722452~~Z",	224	····················"iopub.status.idle":·"2024-05-26T12:10:01.996270Z",
225	····················"shell.execute_reply":·"2024-05-26T09:39:23.~~721594~~Z"	225	····················"shell.execute_reply":·"2024-05-26T12:10:01.995453Z"
226	················},	226	················},
227	················"jupyter":·{	227	················"jupyter":·{
228	····················"outputs_hidden":·false	228	····················"outputs_hidden":·false
229	················}	229	················}
230	············},	230	············},
231	············"outputs":·[	231	············"outputs":·[
232	················{	232	················{
Offset 237, 17 lines modified		Offset 237, 17 lines modified
237	························"-0.020395987154757343\n"	237	························"-0.020395987154757343\n"
238	····················]	238	····················]
239	················},	239	················},
240	················{	240	················{
241	····················"name":·"stderr",	241	····················"name":·"stderr",
242	····················"output_type":·"stream",	242	····················"output_type":·"stream",
243	····················"text":·[	243	····················"text":·[
244	························"/tmp/ipykernel_2~~477353~~/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]`\n",	244	························"/tmp/ipykernel_158670/1000445862.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]`\n",
245	························"··print(mod1.params[1])\n",	245	························"··print(mod1.params[1])\n",
246	························"/tmp/ipykernel_2~~477353~~/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]`\n",	246	························"/tmp/ipykernel_158670/1000445862.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]`\n",
247	························"··print(mod2.params[1]·*·2)\n"	247	························"··print(mod2.params[1]·*·2)\n"
248	····················]	248	····················]
249	················}	249	················}
250	············],	250	············],
251	············"source":·[	251	············"source":·[
252	················"print(mod1.params[1])\n",	252	················"print(mod1.params[1])\n",
253	················"print(mod2.params[1]·*·2)"	253	················"print(mod2.params[1]·*·2)"


Offset 18, 18 lines modified		Offset 18, 18 lines modified
18	············]	18	············]
19	········},	19	········},
20	········{	20	········{
21	············"cell_type":·"code",	21	············"cell_type":·"code",
22	············"execution_count":·1,	22	············"execution_count":·1,
23	············"metadata":·{	23	············"metadata":·{
24	················"execution":·{	24	················"execution":·{
25	····················"iopub.execute_input":·"2024-05-26T09:39:06.~~4232~~76Z",	25	····················"iopub.execute_input":·"2024-05-26T12:09:48.651479Z",
26	····················"iopub.status.busy":·"2024-05-26T09:39:06.~~422967~~Z",	26	····················"iopub.status.busy":·"2024-05-26T12:09:48.651144Z",
27	····················"iopub.status.idle":·"2024-05-26T09:39:09.46~~562~~1Z",	27	····················"iopub.status.idle":·"2024-05-26T12:09:50.768301Z",
28	····················"shell.execute_reply":·"2024-05-26T09:39:09.~~449609~~Z"	28	····················"shell.execute_reply":·"2024-05-26T12:09:50.767475Z"
29	················}	29	················}
30	············},	30	············},
31	············"outputs":·[],	31	············"outputs":·[],
32	············"source":·[	32	············"source":·[
33	················"import·pandas·as·pd\n",	33	················"import·pandas·as·pd\n",
34	················"import·numpy·as·np\n",	34	················"import·numpy·as·np\n",
35	················"import·statsmodels.api·as·sm\n",	35	················"import·statsmodels.api·as·sm\n",
Offset 44, 18 lines modified		Offset 44, 18 lines modified
44	············]	44	············]
45	········},	45	········},
46	········{	46	········{
47	············"cell_type":·"code",	47	············"cell_type":·"code",
48	············"execution_count":·2,	48	············"execution_count":·2,
49	············"metadata":·{	49	············"metadata":·{
50	················"execution":·{	50	················"execution":·{
51	····················"iopub.execute_input":·"2024-05-26T09:39:09.482859Z",	51	····················"iopub.execute_input":·"2024-05-26T12:09:50.772875Z",
52	····················"iopub.status.busy":·"2024-05-26T09:39:09.482~~418~~Z",	52	····················"iopub.status.busy":·"2024-05-26T12:09:50.772395Z",
53	····················"iopub.status.idle":·"2024-05-26T09:39:09.514~~418~~Z",	53	····················"iopub.status.idle":·"2024-05-26T12:09:50.784256Z",
54	····················"shell.execute_reply":·"2024-05-26T09:39:09.~~501599~~Z"	54	····················"shell.execute_reply":·"2024-05-26T12:09:50.783433Z"
55	················}	55	················}
56	············},	56	············},
57	············"outputs":·[],	57	············"outputs":·[],
58	············"source":·[	58	············"source":·[
59	················"np.random.seed(3424)"	59	················"np.random.seed(3424)"
60	············]	60	············]
61	········},	61	········},
Offset 67, 18 lines modified		Offset 67, 18 lines modified
67	············]	67	············]
68	········},	68	········},
69	········{	69	········{
70	············"cell_type":·"code",	70	············"cell_type":·"code",
71	············"execution_count":·3,	71	············"execution_count":·3,
72	············"metadata":·{	72	············"metadata":·{
73	················"execution":·{	73	················"execution":·{
74	····················"iopub.execute_input":·"2024-05-26T09:39:09.~~522696~~Z",	74	····················"iopub.execute_input":·"2024-05-26T12:09:50.788577Z",
75	····················"iopub.status.busy":·"2024-05-26T09:39:09.~~522382~~Z",	75	····················"iopub.status.busy":·"2024-05-26T12:09:50.788263Z",
76	····················"iopub.status.idle":·"2024-05-26T09:39:09.~~557599~~Z",	76	····················"iopub.status.idle":·"2024-05-26T12:09:50.796247Z",
77	····················"shell.execute_reply":·"2024-05-26T09:39:09.541579Z"	77	····················"shell.execute_reply":·"2024-05-26T12:09:50.795437Z"
78	················}	78	················}
79	············},	79	············},
80	············"outputs":·[],	80	············"outputs":·[],
81	············"source":·[	81	············"source":·[
82	················"n·=·1000"	82	················"n·=·1000"
83	············]	83	············]
84	········},	84	········},
Offset 90, 18 lines modified		Offset 90, 18 lines modified
90	············]	90	············]
91	········},	91	········},
92	········{	92	········{
93	············"cell_type":·"code",	93	············"cell_type":·"code",
94	············"execution_count":·4,	94	············"execution_count":·4,
95	············"metadata":·{	95	············"metadata":·{
96	················"execution":·{	96	················"execution":·{
97	····················"iopub.execute_input":·"2024-05-26T09:39:09.~~5668~~22Z",	97	····················"iopub.execute_input":·"2024-05-26T12:09:50.800628Z",
98	····················"iopub.status.busy":·"2024-05-26T09:39:09.~~56648~~1Z",	98	····················"iopub.status.busy":·"2024-05-26T12:09:50.800311Z",
99	····················"iopub.status.idle":·"2024-05-26T09:39:09.~~601620~~Z",	99	····················"iopub.status.idle":·"2024-05-26T12:09:50.815899Z",
100	····················"shell.execute_reply":·"2024-05-26T09:39:09.~~585586~~Z"	100	····················"shell.execute_reply":·"2024-05-26T12:09:50.811415Z"
101	················},	101	················},
102	················"lines_to_next_cell":·1	102	················"lines_to_next_cell":·1
103	············},	103	············},
104	············"outputs":·[],	104	············"outputs":·[],
105	············"source":·[	105	············"source":·[
106	················"exp·=·np.random.normal(size=n)"	106	················"exp·=·np.random.normal(size=n)"
107	············]	107	············]
Offset 114, 18 lines modified		Offset 114, 18 lines modified
114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·5,	118	············"execution_count":·5,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2024-05-26T09:39:09.610~~754~~Z",	121	····················"iopub.execute_input":·"2024-05-26T12:09:50.820303Z",
122	····················"iopub.status.busy":·"2024-05-26T09:39:09.61~~0433~~Z",	122	····················"iopub.status.busy":·"2024-05-26T12:09:50.819996Z",
123	····················"iopub.status.idle":·"2024-05-26T09:39:09.~~645657~~Z",	123	····················"iopub.status.idle":·"2024-05-26T12:09:50.839781Z",
124	····················"shell.execute_reply":·"2024-05-26T09:39:09.~~629587~~Z"	124	····················"shell.execute_reply":·"2024-05-26T12:09:50.835412Z"
125	················},	125	················},
126	················"lines_to_next_cell":·1	126	················"lines_to_next_cell":·1
127	············},	127	············},
128	············"outputs":·[],	128	············"outputs":·[],
129	············"source":·[	129	············"source":·[
130	················"def·gen_mediator():\n",	130	················"def·gen_mediator():\n",
131	················"····mn·=·np.exp(exp)\n",	131	················"····mn·=·np.exp(exp)\n",
Offset 144, 18 lines modified		Offset 144, 18 lines modified
144	············]	144	············]
145	········},	145	········},
146	········{	146	········{
147	············"cell_type":·"code",	147	············"cell_type":·"code",
148	············"execution_count":·6,	148	············"execution_count":·6,
149	············"metadata":·{	149	············"metadata":·{
150	················"execution":·{	150	················"execution":·{
151	····················"iopub.execute_input":·"2024-05-26T09:39:09.654~~700~~Z",	151	····················"iopub.execute_input":·"2024-05-26T12:09:50.844119Z",
152	····················"iopub.status.busy":·"2024-05-26T09:39:09.654387Z",	152	····················"iopub.status.busy":·"2024-05-26T12:09:50.843798Z",
153	····················"iopub.status.idle":·"2024-05-26T09:39:09.6~~856~~38Z",	153	····················"iopub.status.idle":·"2024-05-26T12:09:50.864183Z",
154	····················"shell.execute_reply":·"2024-05-26T09:39:09.673~~586~~Z"	154	····················"shell.execute_reply":·"2024-05-26T12:09:50.863412Z"
155	················},	155	················},
156	················"lines_to_next_cell":·1	156	················"lines_to_next_cell":·1
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"def·gen_outcome(otype,·mtime0):\n",	160	················"def·gen_outcome(otype,·mtime0):\n",
161	················"····if·otype·==·\"full\":\n",	161	················"····if·otype·==·\"full\":\n",
Offset 180, 18 lines modified		Offset 180, 18 lines modified
180	············]	180	············]
181	········},	181	········},
182	········{	182	········{
183	············"cell_type":·"code",	183	············"cell_type":·"code",
184	············"execution_count":·7,	184	············"execution_count":·7,
185	············"metadata":·{	185	············"metadata":·{
186	················"execution":·{	186	················"execution":·{
187	····················"iopub.execute_input":·"2024-05-26T09:39:09.694690Z",	187	····················"iopub.execute_input":·"2024-05-26T12:09:50.868468Z",
188	····················"iopub.status.busy":·"2024-05-26T09:39:09.~~69438~~5Z",	188	····················"iopub.status.busy":·"2024-05-26T12:09:50.868165Z",
189	····················"iopub.status.idle":·"2024-05-26T09:39:09.~~714359~~Z",	189	····················"iopub.status.idle":·"2024-05-26T12:09:50.880185Z",
190	····················"shell.execute_reply":·"2024-05-26T09:39:09.~~713576~~Z"	190	····················"shell.execute_reply":·"2024-05-26T12:09:50.879418Z"
191	················},	191	················},
192	················"lines_to_next_cell":·1	192	················"lines_to_next_cell":·1
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24	············]	24	············]
25	········},	25	········},
26	········{	26	········{
27	············"cell_type":·"code",	27	············"cell_type":·"code",
28	············"execution_count":·1,	28	············"execution_count":·1,
29	············"metadata":·{	29	············"metadata":·{
30	················"execution":·{	30	················"execution":·{
31	····················"iopub.execute_input":·"2024-05-26T09:39:06.~~170806~~Z",	31	····················"iopub.execute_input":·"2024-05-26T12:09:45.014712Z",
32	····················"iopub.status.busy":·"2024-05-26T09:39:06.~~1704~~95Z",	32	····················"iopub.status.busy":·"2024-05-26T12:09:45.014391Z",
33	····················"iopub.status.idle":·"2024-05-26T09:39:07.~~238454~~Z",	33	····················"iopub.status.idle":·"2024-05-26T12:09:45.901867Z",
34	····················"shell.execute_reply":·"2024-05-26T09:39:07.~~237604~~Z"	34	····················"shell.execute_reply":·"2024-05-26T12:09:45.899476Z"
35	················}	35	················}
36	············},	36	············},
37	············"outputs":·[],	37	············"outputs":·[],
38	············"source":·[	38	············"source":·[
39	················"%matplotlib·inline"	39	················"%matplotlib·inline"
40	············]	40	············]
41	········},	41	········},
42	········{	42	········{
43	············"cell_type":·"code",	43	············"cell_type":·"code",
44	············"execution_count":·2,	44	············"execution_count":·2,
45	············"metadata":·{	45	············"metadata":·{
46	················"execution":·{	46	················"execution":·{
47	····················"iopub.execute_input":·"2024-05-26T09:39:07.~~242880~~Z",	47	····················"iopub.execute_input":·"2024-05-26T12:09:45.910922Z",
48	····················"iopub.status.busy":·"2024-05-26T09:39:07.~~242~~477Z",	48	····················"iopub.status.busy":·"2024-05-26T12:09:45.910468Z",
49	····················"iopub.status.idle":·"2024-05-26T09:39:08.506~~470~~Z",	49	····················"iopub.status.idle":·"2024-05-26T12:09:47.276289Z",
50	····················"shell.execute_reply":·"2024-05-26T09:39:08.505~~608~~Z"	50	····················"shell.execute_reply":·"2024-05-26T12:09:47.275454Z"
51	················}	51	················}
52	············},	52	············},
53	············"outputs":·[],	53	············"outputs":·[],
54	············"source":·[	54	············"source":·[
55	················"import·numpy·as·np\n",	55	················"import·numpy·as·np\n",
56	················"import·pandas·as·pd\n",	56	················"import·pandas·as·pd\n",
57	················"from·scipy·import·stats,·optimize\n",	57	················"from·scipy·import·stats,·optimize\n",
Offset 80, 18 lines modified		Offset 80, 18 lines modified
80	············]	80	············]
81	········},	81	········},
82	········{	82	········{
83	············"cell_type":·"code",	83	············"cell_type":·"code",
84	············"execution_count":·3,	84	············"execution_count":·3,
85	············"metadata":·{	85	············"metadata":·{
86	················"execution":·{	86	················"execution":·{
87	····················"iopub.execute_input":·"2024-05-26T09:39:08.~~510947~~Z",	87	····················"iopub.execute_input":·"2024-05-26T12:09:47.284790Z",
88	····················"iopub.status.busy":·"2024-05-26T09:39:08.~~510500~~Z",	88	····················"iopub.status.busy":·"2024-05-26T12:09:47.284312Z",
89	····················"iopub.status.idle":·"2024-05-26T09:39:08.~~538398~~Z",	89	····················"iopub.status.idle":·"2024-05-26T12:09:47.312256Z",
90	····················"shell.execute_reply":·"2024-05-26T09:39:08.~~537599~~Z"	90	····················"shell.execute_reply":·"2024-05-26T12:09:47.311447Z"
91	················}	91	················}
92	············},	92	············},
93	············"outputs":·[	93	············"outputs":·[
94	················{	94	················{
95	····················"data":·{	95	····················"data":·{
96	························"text/plain":·[	96	························"text/plain":·[
97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
Offset 118, 18 lines modified		Offset 118, 18 lines modified
118	············]	118	············]
119	········},	119	········},
120	········{	120	········{
121	············"cell_type":·"code",	121	············"cell_type":·"code",
122	············"execution_count":·4,	122	············"execution_count":·4,
123	············"metadata":·{	123	············"metadata":·{
124	················"execution":·{	124	················"execution":·{
125	····················"iopub.execute_input":·"2024-05-26T09:39:08.~~5426~~26Z",	125	····················"iopub.execute_input":·"2024-05-26T12:09:47.320524Z",
126	····················"iopub.status.busy":·"2024-05-26T09:39:08.542324Z",	126	····················"iopub.status.busy":·"2024-05-26T12:09:47.320210Z",
127	····················"iopub.status.idle":·"2024-05-26T09:39:08.562434Z",	127	····················"iopub.status.idle":·"2024-05-26T12:09:47.356229Z",
128	····················"shell.execute_reply":·"2024-05-26T09:39:08.~~561599~~Z"	128	····················"shell.execute_reply":·"2024-05-26T12:09:47.355434Z"
129	················}	129	················}
130	············},	130	············},
131	············"outputs":·[	131	············"outputs":·[
132	················{	132	················{
133	····················"data":·{	133	····················"data":·{
134	························"text/plain":·[	134	························"text/plain":·[
135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
Offset 149, 18 lines modified		Offset 149, 18 lines modified
149	············]	149	············]
150	········},	150	········},
151	········{	151	········{
152	············"cell_type":·"code",	152	············"cell_type":·"code",
153	············"execution_count":·5,	153	············"execution_count":·5,
154	············"metadata":·{	154	············"metadata":·{
155	················"execution":·{	155	················"execution":·{
156	····················"iopub.execute_input":·"2024-05-26T09:39:08.56~~6801~~Z",	156	····················"iopub.execute_input":·"2024-05-26T12:09:47.364716Z",
157	····················"iopub.status.busy":·"2024-05-26T09:39:08.566490Z",	157	····················"iopub.status.busy":·"2024-05-26T12:09:47.364404Z",
158	····················"iopub.status.idle":·"2024-05-26T09:39:08.578418Z",	158	····················"iopub.status.idle":·"2024-05-26T12:09:47.372215Z",
159	····················"shell.execute_reply":·"2024-05-26T09:39:08.57~~760~~2Z"	159	····················"shell.execute_reply":·"2024-05-26T12:09:47.371442Z"
160	················}	160	················}
161	············},	161	············},
162	············"outputs":·[	162	············"outputs":·[
163	················{	163	················{
164	····················"data":·{	164	····················"data":·{
165	························"text/plain":·[	165	························"text/plain":·[
166	····························"array([120,·130,··80,·400,··95,·170])"	166	····························"array([120,·130,··80,·400,··95,·170])"
Offset 183, 18 lines modified		Offset 183, 18 lines modified
183	············]	183	············]
184	········},	184	········},
185	········{	185	········{
186	············"cell_type":·"code",	186	············"cell_type":·"code",
187	············"execution_count":·6,	187	············"execution_count":·6,
188	············"metadata":·{	188	············"metadata":·{
189	················"execution":·{	189	················"execution":·{
190	····················"iopub.execute_input":·"2024-05-26T09:39:08.582627Z",	190	····················"iopub.execute_input":·"2024-05-26T12:09:47.380646Z",
191	····················"iopub.status.busy":·"2024-05-26T09:39:08.582322Z",	191	····················"iopub.status.busy":·"2024-05-26T12:09:47.380304Z",
192	····················"iopub.status.idle":·"2024-05-26T09:39:08.59~~4418~~Z",	192	····················"iopub.status.idle":·"2024-05-26T12:09:47.392252Z",
193	····················"shell.execute_reply":·"2024-05-26T09:39:08.59~~3596~~Z"	193	····················"shell.execute_reply":·"2024-05-26T12:09:47.391444Z"
194	················}	194	················}
195	············},	195	············},
196	············"outputs":·[],	196	············"outputs":·[],
197	············"source":·[	197	············"source":·[
198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"	198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"
199	············]	199	············]
200	········},	200	········},
Offset 209, 18 lines modified		Offset 209, 18 lines modified
209	············]	209	············]
210	········},	210	········},
211	········{	211	········{
212	············"cell_type":·"code",	212	············"cell_type":·"code",
213	············"execution_count":·7,	213	············"execution_count":·7,
214	············"metadata":·{	214	············"metadata":·{
215	················"execution":·{	215	················"execution":·{
216	····················"iopub.execute_input":·"2024-05-26T09:39:08.~~598636~~Z",	216	····················"iopub.execute_input":·"2024-05-26T12:09:47.400500Z",
217	····················"iopub.status.busy":·"2024-05-26T09:39:08.~~598337~~Z",	217	····················"iopub.status.busy":·"2024-05-26T12:09:47.400201Z",
218	····················"iopub.status.idle":·"2024-05-26T09:39:08.624~~736~~Z",	218	····················"iopub.status.idle":·"2024-05-26T12:09:47.424225Z",
219	····················"shell.execute_reply":·"2024-05-26T09:39:08.621637Z"	219	····················"shell.execute_reply":·"2024-05-26T12:09:47.423436Z"
220	················}	220	················}
221	············},	221	············},
222	············"outputs":·[	222	············"outputs":·[
223	················{	223	················{
224	····················"name":·"stdout",	224	····················"name":·"stdout",
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Offset 799, 15 lines modified		Offset 799, 15 lines modified
799	</div>	799	</div>
800	</div>	800	</div>
801	<div·class="nboutput·docutils·container">	801	<div·class="nboutput·docutils·container">
802	<div·class="prompt·empty·docutils·container">	802	<div·class="prompt·empty·docutils·container">
803	</div>	803	</div>
804	<div·class="output_area·stderr·docutils·container">	804	<div·class="output_area·stderr·docutils·container">
805	<div·class="highlight"><pre>	805	<div·class="highlight"><pre>
806	/tmp/ipykernel_2460~~648~~/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be·used·together·with·FixedLocator	806	/tmp/ipykernel_156817/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be·used·together·with·FixedLocator
807	··ax.set_xticklabels(dta.columns.values[::10])	807	··ax.set_xticklabels(dta.columns.values[::10])
808	</pre></div></div>	808	</pre></div></div>
809	</div>	809	</div>
810	<div·class="nboutput·nblast·docutils·container">	810	<div·class="nboutput·nblast·docutils·container">
811	<div·class="prompt·empty·docutils·container">	811	<div·class="prompt·empty·docutils·container">
812	</div>	812	</div>
813	<div·class="output_area·docutils·container">	813	<div·class="output_area·docutils·container">


Offset 126, 15 lines modified		Offset 126, 15 lines modified
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_2460~~648~~/427128218.py:3:·UserWarning:·FixedFormatter·should·only	133	/tmp/ipykernel_156817/427128218.py:3:·UserWarning:·FixedFormatter·should·only
134	be·used·together·with·FixedLocator	134	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·trajectories	137	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories
138	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience	138	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]:


Offset 578, 19 lines modified		Offset 578, 19 lines modified
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_2456~~428~~/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_156054/976557282.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('var.level·····=·%.5f'·%·res.params[0])	586	··print('var.level·····=·%.5f'·%·res.params[0])
587	/tmp/ipykernel_2456~~428~~/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_156054/976557282.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('var.irregular·=·%.5f'·%·res.params[1])	588	··print('var.irregular·=·%.5f'·%·res.params[1])
589	/tmp/ipykernel_2456~~428~~/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_156054/976557282.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('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))	590	··print('h··scale·····=·%.5f'·%·(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>


Offset 242, 25 lines modified		Offset 242, 25 lines modified
242	Original·model	242	Original·model
243	var.level·····=·0.74469	243	var.level·····=·0.74469
244	var.irregular·=·3.37330	244	var.irregular·=·3.37330

245	Concentrated·model	245	Concentrated·model
246	scale·········=·0.74472	246	scale·········=·0.74472
247	h·*·scale·····=·3.37338	247	h·*·scale·····=·3.37338
248	/tmp/ipykernel_2456~~428~~/976557282.py:2:·FutureWarning:·Series.__getitem__	248	/tmp/ipykernel_156054/976557282.py:2:·FutureWarning:·Series.__getitem__
249	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	249	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
250	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	250	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_2456~~428~~/976557282.py:3:·FutureWarning:·Series.__getitem__	253	/tmp/ipykernel_156054/976557282.py:3:·FutureWarning:·Series.__getitem__
254	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	254	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
255	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	255	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_2456~~428~~/976557282.py:7:·FutureWarning:·Series.__getitem__	258	/tmp/ipykernel_156054/976557282.py:7:·FutureWarning:·Series.__getitem__
259	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	259	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
260	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	260	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·numerically	264	By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically
265	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow	265	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow


Offset 50, 35 lines modified		Offset 50, 35 lines modified
50	········},	50	········},
51	········{	51	········{
52	············"cell_type":·"code",	52	············"cell_type":·"code",
53	············"execution_count":·1,	53	············"execution_count":·1,
54	············"id":·"ba21553a-e571-42ac-b166-b625a50509fe",	54	············"id":·"ba21553a-e571-42ac-b166-b625a50509fe",
55	············"metadata":·{	55	············"metadata":·{
56	················"execution":·{	56	················"execution":·{
57	····················"iopub.execute_input":·"2024-05-26T09:38:31.~~545399~~Z",	57	····················"iopub.execute_input":·"2024-05-26T12:09:18.328501Z",
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60	····················"shell.execute_reply":·"2024-05-26T09:38:32.733~~600~~Z"	60	····················"shell.execute_reply":·"2024-05-26T12:09:19.043472Z"
61	················}	61	················}
62	············},	62	············},
63	············"outputs":·[],	63	············"outputs":·[],
64	············"source":·[	64	············"source":·[
65	················"%matplotlib·inline"	65	················"%matplotlib·inline"
66	············]	66	············]
67	········},	67	········},
68	········{	68	········{
69	············"cell_type":·"code",	69	············"cell_type":·"code",
70	············"execution_count":·2,	70	············"execution_count":·2,
71	············"id":·"fe284c44-b750-4e6e-94d0-b238f364cd7b",	71	············"id":·"fe284c44-b750-4e6e-94d0-b238f364cd7b",
72	············"metadata":·{	72	············"metadata":·{
73	················"execution":·{	73	················"execution":·{
74	····················"iopub.execute_input":·"2024-05-26T09:38:32.~~738584~~Z",	74	····················"iopub.execute_input":·"2024-05-26T12:09:19.052901Z",
75	····················"iopub.status.busy":·"2024-05-26T09:38:32.~~738203~~Z",	75	····················"iopub.status.busy":·"2024-05-26T12:09:19.052467Z",
76	····················"iopub.status.idle":·"2024-05-26T09:38:33.210421Z",	76	····················"iopub.status.idle":·"2024-05-26T12:09:19.424284Z",
77	····················"shell.execute_reply":·"2024-05-26T09:38:33.~~209601~~Z"	77	····················"shell.execute_reply":·"2024-05-26T12:09:19.423443Z"
78	················}	78	················}
79	············},	79	············},
80	············"outputs":·[],	80	············"outputs":·[],
81	············"source":·[	81	············"source":·[
82	················"import·numpy·as·np\n",	82	················"import·numpy·as·np\n",
83	················"import·pandas·as·pd\n",	83	················"import·pandas·as·pd\n",
84	················"\n",	84	················"\n",
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95	········},	95	········},
96	········{	96	········{
97	············"cell_type":·"code",	97	············"cell_type":·"code",
98	············"execution_count":·3,	98	············"execution_count":·3,
99	············"id":·"f02b87c6-ee8f-4bb1-bf08-d252b9277733",	99	············"id":·"f02b87c6-ee8f-4bb1-bf08-d252b9277733",
100	············"metadata":·{	100	············"metadata":·{
101	················"execution":·{	101	················"execution":·{
102	····················"iopub.execute_input":·"2024-05-26T09:38:33.~~218922~~Z",	102	····················"iopub.execute_input":·"2024-05-26T12:09:19.432796Z",
103	····················"iopub.status.busy":·"2024-05-26T09:38:33.~~218516~~Z",	103	····················"iopub.status.busy":·"2024-05-26T12:09:19.432335Z",
104	····················"iopub.status.idle":·"2024-05-26T09:38:34.~~361199~~Z",	104	····················"iopub.status.idle":·"2024-05-26T12:09:20.448237Z",
105	····················"shell.execute_reply":·"2024-05-26T09:38:34.~~360~~411Z"	105	····················"shell.execute_reply":·"2024-05-26T12:09:20.447440Z"
106	················}	106	················}
107	············},	107	············},
108	············"outputs":·[],	108	············"outputs":·[],
109	············"source":·[	109	············"source":·[
110	················"from·statsmodels.tsa.api·import·SARIMAX,·AutoReg\n",	110	················"from·statsmodels.tsa.api·import·SARIMAX,·AutoReg\n",
111	················"from·statsmodels.tsa.arima.model·import·ARIMA"	111	················"from·statsmodels.tsa.arima.model·import·ARIMA"
112	············]	112	············]
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121	········},	121	········},
122	········{	122	········{
123	············"cell_type":·"code",	123	············"cell_type":·"code",
124	············"execution_count":·4,	124	············"execution_count":·4,
125	············"id":·"7200d248-bd47-4c95-9f1c-6daaf1e09bb1",	125	············"id":·"7200d248-bd47-4c95-9f1c-6daaf1e09bb1",
126	············"metadata":·{	126	············"metadata":·{
127	················"execution":·{	127	················"execution":·{
128	····················"iopub.execute_input":·"2024-05-26T09:38:34.~~374881~~Z",	128	····················"iopub.execute_input":·"2024-05-26T12:09:20.456759Z",
129	····················"iopub.status.busy":·"2024-05-26T09:38:34.~~374433~~Z",	129	····················"iopub.status.busy":·"2024-05-26T12:09:20.456287Z",
130	····················"iopub.status.idle":·"2024-05-26T09:38:34.~~958470~~Z",	130	····················"iopub.status.idle":·"2024-05-26T12:09:21.060208Z",
131	····················"shell.execute_reply":·"2024-05-26T09:38:34.95~~7616~~Z"	131	····················"shell.execute_reply":·"2024-05-26T12:09:21.059423Z"
132	················}	132	················}
133	············},	133	············},
134	············"outputs":·[	134	············"outputs":·[
135	················{	135	················{
136	····················"name":·"stdout",	136	····················"name":·"stdout",
137	····················"output_type":·"stream",	137	····················"output_type":·"stream",
138	····················"text":·[	138	····················"text":·[
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220	········},	220	········},
221	········{	221	········{
222	············"cell_type":·"code",	222	············"cell_type":·"code",
223	············"execution_count":·5,	223	············"execution_count":·5,
224	············"id":·"8ff07d0e-6754-4664-93e4-0f9299096868",	224	············"id":·"8ff07d0e-6754-4664-93e4-0f9299096868",
225	············"metadata":·{	225	············"metadata":·{
226	················"execution":·{	226	················"execution":·{
227	····················"iopub.execute_input":·"2024-05-26T09:38:34.96~~2880~~Z",	227	····················"iopub.execute_input":·"2024-05-26T12:09:21.064642Z",
228	····················"iopub.status.busy":·"2024-05-26T09:38:34.96~~2553~~Z",	228	····················"iopub.status.busy":·"2024-05-26T12:09:21.064329Z",
229	····················"iopub.status.idle":·"2024-05-26T09:38:35.002~~478~~Z",	229	····················"iopub.status.idle":·"2024-05-26T12:09:21.132156Z",
230	····················"shell.execute_reply":·"2024-05-26T09:38:35.001~~614~~Z"	230	····················"shell.execute_reply":·"2024-05-26T12:09:21.131402Z"
231	················}	231	················}
232	············},	232	············},
233	············"outputs":·[	233	············"outputs":·[
234	················{	234	················{
235	····················"data":·{	235	····················"data":·{
236	························"text/html":·[	236	························"text/html":·[
237	····························"<div>\n",	237	····························"<div>\n",
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339	········},	339	········},
340	········{	340	········{
341	············"cell_type":·"code",	341	············"cell_type":·"code",
342	············"execution_count":·6,	342	············"execution_count":·6,
343	············"id":·"c18adf81-1ad9-4d11-a23b-e6d139c1fa3e",	343	············"id":·"c18adf81-1ad9-4d11-a23b-e6d139c1fa3e",
344	············"metadata":·{	344	············"metadata":·{
345	················"execution":·{	345	················"execution":·{
346	····················"iopub.execute_input":·"2024-05-26T09:38:35.~~010798~~Z",	346	····················"iopub.execute_input":·"2024-05-26T12:09:21.136570Z",
347	····················"iopub.status.busy":·"2024-05-26T09:38:35.~~010482~~Z",	347	····················"iopub.status.busy":·"2024-05-26T12:09:21.136261Z",
348	····················"iopub.status.idle":·"2024-05-26T09:38:35.298~~425~~Z",	348	····················"iopub.status.idle":·"2024-05-26T12:09:21.468231Z",
349	····················"shell.execute_reply":·"2024-05-26T09:38:35.297~~607~~Z"	349	····················"shell.execute_reply":·"2024-05-26T12:09:21.467445Z"
350	················}	350	················}
351	············},	351	············},
352	············"outputs":·[	352	············"outputs":·[
353	················{	353	················{
354	····················"name":·"stdout",	354	····················"name":·"stdout",
355	····················"output_type":·"stream",	355	····················"output_type":·"stream",
356	····················"text":·[	356	····················"text":·[
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378	························"\n",	378	························"\n",
379	························"·············*\n",	379	························"·············*\n",
380	························"\n",	380	························"\n",
381	························"···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F\n",	381	························"···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F\n",
382	························"····3······1······4······1·····0·····0···4.752D-05···1.414D+00\n",	382	························"····3······1······4······1·····0·····0···4.752D-05···1.414D+00\n",
383	························"··F·=···1.4137311099487528·····\n",	383	························"··F·=···1.4137311099487528·····\n",
384	························"\n",	384	························"\n",
385	························"CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH·············\n",	385	························"CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH·············\n"
		386	····················]
		387	················},
		388	················{
		389	····················"name":·"stdout",
		390	····················"output_type":·"stream",
		391	····················"text":·[
386	························"·······························SARIMAX·Results································\n",	392	························"·······························SARIMAX·Results································\n",
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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_~~24436~~87/1512460390.py:6:·InterpolationWarning:·The·test·statistic·is·outside·of·the·range·of·p-values·available·in·the	588	/tmp/ipykernel_155208/1512460390.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="c",·nlags="auto")	590	··kpsstest·=·kpss(timeseries,·regression="c",·nlags="auto")
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>


Offset 172, 16 lines modified		Offset 172, 16 lines modified
172	p-value··················0.100000	172	p-value··················0.100000
173	Lags·Used················0.000000	173	Lags·Used················0.000000
174	Critical·Value·(10%)·····0.347000	174	Critical·Value·(10%)·····0.347000
175	Critical·Value·(5%)······0.463000	175	Critical·Value·(5%)······0.463000
176	Critical·Value·(2.5%)····0.574000	176	Critical·Value·(2.5%)····0.574000
177	Critical·Value·(1%)······0.739000	177	Critical·Value·(1%)······0.739000
178	dtype:·float64	178	dtype:·float64
179	/tmp/ipykernel_~~24436~~87/1512460390.py:6:·InterpolationWarning:·The·test	179	/tmp/ipykernel_155208/1512460390.py:6:·InterpolationWarning:·The·test·statistic
180	~~statistic·~~is·outside·of·the·range·of·p-values·available·in·the	180	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·ADF	186	Two·tests·for·checking·the·stationarity·of·a·time·series·are·used,·namely·ADF


Offset 21, 18 lines modified		Offset 21, 18 lines modified
21	········},	21	········},
22	········{	22	········{
23	············"cell_type":·"code",	23	············"cell_type":·"code",
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25	············"id":·"59f2450e",	25	············"id":·"59f2450e",
26	············"metadata":·{	26	············"metadata":·{
27	················"execution":·{	27	················"execution":·{
28	····················"iopub.execute_input":·"2024-05-26T09:38:22.~~306726~~Z",	28	····················"iopub.execute_input":·"2024-05-26T12:09:10.832359Z",
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36	················"import·numpy·as·np\n",	36	················"import·numpy·as·np\n",
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38	················"import·numpy·as·np\n",	38	················"import·numpy·as·np\n",
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158	················}	158	················}
159	············},	159	············},
160	············"outputs":·[	160	············"outputs":·[
161	················{	161	················{
162	····················"data":·{	162	····················"data":·{
163	························"text/plain":·[	163	························"text/plain":·[
164	····························"['conf_int',\n",	164	····························"['conf_int',\n",
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180	········},	180	········},
181	········{	181	········{
182	············"cell_type":·"code",	182	············"cell_type":·"code",
183	············"execution_count":·5,	183	············"execution_count":·5,
184	············"id":·"76be72c9",	184	············"id":·"76be72c9",
185	············"metadata":·{	185	············"metadata":·{
186	················"execution":·{	186	················"execution":·{
187	····················"iopub.execute_input":·"2024-05-26T09:38:22.2~~34704~~Z",	187	····················"iopub.execute_input":·"2024-05-26T12:09:11.288280Z",
188	····················"iopub.status.busy":·"2024-05-26T09:38:22.2~~34400~~Z",	188	····················"iopub.status.busy":·"2024-05-26T12:09:11.287979Z",
189	····················"iopub.status.idle":·"2024-05-26T09:38:22.~~293988~~Z",	189	····················"iopub.status.idle":·"2024-05-26T12:09:11.304212Z",
190	····················"shell.execute_reply":·"2024-05-26T09:38:22.~~281598~~Z"	190	····················"shell.execute_reply":·"2024-05-26T12:09:11.303436Z"
191	················}	191	················}
192	············},	192	············},
193	············"outputs":·[	193	············"outputs":·[
194	················{	194	················{
195	····················"name":·"stdout",	195	····················"name":·"stdout",
196	····················"output_type":·"stream",	196	····················"output_type":·"stream",
197	····················"text":·[	197	····················"text":·[
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210	········},	210	········},
211	········{	211	········{
212	············"cell_type":·"code",	212	············"cell_type":·"code",
213	············"execution_count":·6,	213	············"execution_count":·6,
214	············"id":·"18025e2a",	214	············"id":·"18025e2a",
215	············"metadata":·{	215	············"metadata":·{
216	················"execution":·{	216	················"execution":·{
217	····················"iopub.execute_input":·"2024-05-26T09:38:22.30~~1065~~Z",	217	····················"iopub.execute_input":·"2024-05-26T12:09:11.308307Z",
218	····················"iopub.status.busy":·"2024-05-26T09:38:22.30~~075~~4Z",	218	····················"iopub.status.busy":·"2024-05-26T12:09:11.308014Z",
219	····················"iopub.status.idle":·"2024-05-26T09:38:22.3~~18425~~Z",	219	····················"iopub.status.idle":·"2024-05-26T12:09:11.320170Z",
220	····················"shell.execute_reply":·"2024-05-26T09:38:22.31~~7604~~Z"	220	····················"shell.execute_reply":·"2024-05-26T12:09:11.319432Z"
221	················}	221	················}
222	············},	222	············},
223	············"outputs":·[	223	············"outputs":·[
224	················{	224	················{
225	····················"data":·{	225	····················"data":·{
226	························"text/plain":·[	226	························"text/plain":·[
227	····························"(0.3816117144128266,·0.529937017229363)"	227	····························"(0.3816117144128266,·0.529937017229363)"
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239	········},	239	········},
240	········{	240	········{
241	············"cell_type":·"code",	241	············"cell_type":·"code",
242	············"execution_count":·7,	242	············"execution_count":·7,
243	············"id":·"bd85c9be",	243	············"id":·"bd85c9be",
244	············"metadata":·{	244	············"metadata":·{
245	················"execution":·{	245	················"execution":·{
246	····················"iopub.execute_input":·"2024-05-26T09:38:22.32~~2679~~Z",	246	····················"iopub.execute_input":·"2024-05-26T12:09:11.324245Z",
247	····················"iopub.status.busy":·"2024-05-26T09:38:22.32~~2375~~Z",	247	····················"iopub.status.busy":·"2024-05-26T12:09:11.323941Z",
248	····················"iopub.status.idle":·"2024-05-26T09:38:22.3~~38439~~Z",	248	····················"iopub.status.idle":·"2024-05-26T12:09:11.340188Z",
249	····················"shell.execute_reply":·"2024-05-26T09:38:22.33~~7605~~Z"	249	····················"shell.execute_reply":·"2024-05-26T12:09:11.339434Z"
250	················}	250	················}
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Offset 889, 15 lines modified		Offset 889, 15 lines modified
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	~~351~~·ms·±·59.3·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·each)	896	224·ms·±·61.9·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·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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925	</div>	925	</div>
926	</div>	926	</div>
927	<div·class="nboutput·docutils·container">	927	<div·class="nboutput·docutils·container">
928	<div·class="prompt·empty·docutils·container">	928	<div·class="prompt·empty·docutils·container">
929	</div>	929	</div>
930	<div·class="output_area·docutils·container">	930	<div·class="output_area·docutils·container">
931	<div·class="highlight"><pre>	931	<div·class="highlight"><pre>
932	23.8·ms·±·4.11·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)	932	18.1·ms·±·3.65·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)
933	</pre></div></div>	933	</pre></div></div>
934	</div>	934	</div>
935	<div·class="nboutput·nblast·docutils·container">	935	<div·class="nboutput·nblast·docutils·container">
936	<div·class="prompt·empty·docutils·container">	936	<div·class="prompt·empty·docutils·container">
937	</div>	937	</div>
938	<div·class="output_area·docutils·container">	938	<div·class="output_area·docutils·container">
939	<img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png"·/>	939	<img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png"·/>


Offset 493, 15 lines modified		Offset 493, 15 lines modified
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	~~351~~·ms·±·59.3·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·each)	500	224·ms·±·61.9·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·1·loop·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·linear	502	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(
Offset 511, 15 lines modified		Offset 511, 15 lines modified
511	····seasonal_jump=seasonal_jump,	511	····seasonal_jump=seasonal_jump,
512	····trend_jump=trend_jump,	512	····trend_jump=trend_jump,
513	····low_pass_jump=low_pass_jump,	513	····low_pass_jump=low_pass_jump,
514	)	514	)
515	%timeit·mod.fit()	515	%timeit·mod.fit()
516	res·=·mod.fit()	516	res·=·mod.fit()
517	fig·=·res.plot(observed=False,·resid=False)	517	fig·=·res.plot(observed=False,·resid=False)
518	23.8·ms·±·4.11·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)	518	18.1·ms·±·3.65·ms·per·loop·(mean·±·std.·dev.·of·7·runs,·10·loops·each)
519	[../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png]	519	[../../../_images/examples_notebooks_generated_stl_decomposition_19_1.png]
520	\x8\x8\x8\x8\x8·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·S\x8ST\x8TL\x8L_\x8?\x8¶·\x8\x8\x8\x8\x8	520	\x8\x8\x8\x8\x8·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·S\x8ST\x8TL\x8L_\x8?\x8¶·\x8\x8\x8\x8\x8
521	STLForecast·simplifies·the·process·of·using·STL·to·remove·seasonalities·and	521	STLForecast·simplifies·the·process·of·using·STL·to·remove·seasonalities·and
522	then·using·a·standard·time-series·model·to·forecast·the·trend·and·cyclical	522	then·using·a·standard·time-series·model·to·forecast·the·trend·and·cyclical
523	components.	523	components.
524	Here·we·use·STL·to·handle·the·seasonality·and·then·an·ARIMA(1,1,0)·to·model·the	524	Here·we·use·STL·to·handle·the·seasonality·and·then·an·ARIMA(1,1,0)·to·model·the
525	deseasonalized·data.·The·seasonal·component·is·forecast·from·the·find·full	525	deseasonalized·data.·The·seasonal·component·is·forecast·from·the·find·full