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| 1 | Package:·python-statsmodels-doc | 1 | Package:·python-statsmodels-doc |
| 2 | Source:·statsmodels | 2 | Source:·statsmodels |
| 3 | Version:·0.14.1+dfsg-2 | 3 | Version:·0.14.1+dfsg-2 |
| 4 | Architecture:·all | 4 | Architecture:·all |
| 5 | Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org> | 5 | Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org> |
| 6 | Installed-Size:·155 | 6 | Installed-Size:·155904 |
| 7 | Depends:·libjs-sphinxdoc·(>=·7.2.2),·libjs-requirejs,·libjs-mathjax | 7 | Depends:·libjs-sphinxdoc·(>=·7.2.2),·libjs-requirejs,·libjs-mathjax |
| 8 | Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc | 8 | Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc |
| 9 | Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~) | 9 | Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~) |
| 10 | Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~) | 10 | Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~) |
| 11 | Section:·doc | 11 | Section:·doc |
| 12 | Priority:·optional | 12 | Priority:·optional |
| 13 | Homepage:·https://www.statsmodels.org | 13 | Homepage:·https://www.statsmodels.org |
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| 182 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_25_1.png | 182 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_25_1.png |
| 183 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_26_1.png | 183 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_26_1.png |
| 184 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_55_0.png | 184 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_55_0.png |
| 185 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_58_1.png | 185 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_58_1.png |
| 186 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_62_1.png | 186 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_62_1.png |
| 187 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_64_0.png | 187 | usr/share/doc/python-statsmodels-doc/html/_images/examples_notebooks_generated_discrete_choice_example_64_0.png |
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| 24 | ················"import·numpy·as·np\n", | 24 | ················"import·numpy·as·np\n", |
| 25 | ················"import·seaborn·as·sns\n", | 25 | ················"import·seaborn·as·sns\n", |
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| 37 | ········}, | 37 | ········}, |
| 38 | ········{ | 38 | ········{ |
| 39 | ············"cell_type":·"code", | 39 | ············"cell_type":·"code", |
| 40 | ············"execution_count":·1, | 40 | ············"execution_count":·1, |
| 41 | ············"id":·"eed890e6", | 41 | ············"id":·"eed890e6", |
| 42 | ············"metadata":·{ | 42 | ············"metadata":·{ |
| 43 | ················"execution":·{ | 43 | ················"execution":·{ |
| 44 | ····················"iopub.execute_input":·"202 | 44 | ····················"iopub.execute_input":·"2025-05-17T08:05:28.308427Z", |
| 45 | ····················"iopub.status.busy":·"202 | 45 | ····················"iopub.status.busy":·"2025-05-17T08:05:28.307947Z", |
| 46 | ····················"iopub.status.idle":·"202 | 46 | ····················"iopub.status.idle":·"2025-05-17T08:05:29.471091Z", |
| 47 | ····················"shell.execute_reply":·"202 | 47 | ····················"shell.execute_reply":·"2025-05-17T08:05:29.469965Z" |
| 48 | ················} | 48 | ················} |
| 49 | ············}, | 49 | ············}, |
| 50 | ············"outputs":·[], | 50 | ············"outputs":·[], |
| 51 | ············"source":·[ | 51 | ············"source":·[ |
| 52 | ················"import·numpy·as·np\n", | 52 | ················"import·numpy·as·np\n", |
| 53 | ················"import·pandas·as·pd\n", | 53 | ················"import·pandas·as·pd\n", |
| 54 | ················"\n", | 54 | ················"\n", |
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| 8 | ············] | 8 | ············] |
| 9 | ········}, | 9 | ········}, |
| 10 | ········{ | 10 | ········{ |
| 11 | ············"cell_type":·"code", | 11 | ············"cell_type":·"code", |
| 12 | ············"execution_count":·1, | 12 | ············"execution_count":·1, |
| 13 | ············"metadata":·{ | 13 | ············"metadata":·{ |
| 14 | ················"execution":·{ | 14 | ················"execution":·{ |
| 15 | ····················"iopub.execute_input":·"202 | 15 | ····················"iopub.execute_input":·"2025-05-17T08:05:15.286446Z", |
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| 19 | ················} | 19 | ················} |
| 20 | ············}, | 20 | ············}, |
| 21 | ············"outputs":·[], | 21 | ············"outputs":·[], |
| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"import·matplotlib.pyplot·as·plt\n", | 23 | ················"import·matplotlib.pyplot·as·plt\n", |
| 24 | ················"import·numpy·as·np\n", | 24 | ················"import·numpy·as·np\n", |
| 25 | ················"import·pandas·as·pd\n", | 25 | ················"import·pandas·as·pd\n", |
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| 22 | ············] | 22 | ············] |
| 23 | ········}, | 23 | ········}, |
| 24 | ········{ | 24 | ········{ |
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| 27 | ············"metadata":·{ | 27 | ············"metadata":·{ |
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| 33 | ················} | 33 | ················} |
| 34 | ············}, | 34 | ············}, |
| 35 | ············"outputs":·[], | 35 | ············"outputs":·[], |
| 36 | ············"source":·[ | 36 | ············"source":·[ |
| 37 | ················"%matplotlib·inline" | 37 | ················"%matplotlib·inline" |
| 38 | ············] | 38 | ············] |
| 39 | ········}, | 39 | ········}, |
| 40 | ········{ | 40 | ········{ |
| 41 | ············"cell_type":·"code", | 41 | ············"cell_type":·"code", |
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| 43 | ············"metadata":·{ | 43 | ············"metadata":·{ |
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| 48 | ····················"shell.execute_reply":·"202 | 48 | ····················"shell.execute_reply":·"2025-05-17T08:05:37.801549Z" |
| 49 | ················} | 49 | ················} |
| 50 | ············}, | 50 | ············}, |
| 51 | ············"outputs":·[], | 51 | ············"outputs":·[], |
| 52 | ············"source":·[ | 52 | ············"source":·[ |
| 53 | ················"import·matplotlib.pyplot·as·plt\n", | 53 | ················"import·matplotlib.pyplot·as·plt\n", |
| 54 | ················"import·numpy·as·np\n", | 54 | ················"import·numpy·as·np\n", |
| 55 | ················"import·pandas·as·pd\n", | 55 | ················"import·pandas·as·pd\n", |
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| 8 | ············] | 8 | ············] |
| 9 | ········}, | 9 | ········}, |
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| 11 | ············"cell_type":·"code", | 11 | ············"cell_type":·"code", |
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| 20 | ················"jupyter":·{ | 20 | ················"jupyter":·{ |
| 21 | ····················"outputs_hidden":·false | 21 | ····················"outputs_hidden":·false |
| 22 | ················} | 22 | ················} |
| 23 | ············}, | 23 | ············}, |
| 24 | ············"outputs":·[], | 24 | ············"outputs":·[], |
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| 10 | ············] | 10 | ············] |
| 11 | ········}, | 11 | ········}, |
| 12 | ········{ | 12 | ········{ |
| 13 | ············"cell_type":·"code", | 13 | ············"cell_type":·"code", |
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| 15 | ············"metadata":·{ | 15 | ············"metadata":·{ |
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| 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", |
| Offset 454, 14 lines modified | Offset 454, 32 lines modified | ||
| 454 | <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span> | 454 | <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span> |
| 455 | </pre></div> | 455 | </pre></div> |
| 456 | </div> | 456 | </div> |
| 457 | </div> | 457 | </div> |
| 458 | <div·class="nboutput·docutils·container"> | 458 | <div·class="nboutput·docutils·container"> |
| 459 | <div·class="prompt·empty·docutils·container"> | 459 | <div·class="prompt·empty·docutils·container"> |
| 460 | </div> | 460 | </div> |
| 461 | <div·class="output_area·stderr·docutils·container"> | ||
| 462 | <div·class="highlight"><pre> | ||
| 463 | /usr/lib/python3/dist-packages/statsmodels/tsa/exponential_smoothing/ets.py:437:·UserWarning:·ETSModel·can·give·wrong·results·on·32·bit·i386 | ||
| 464 | ··warnings.warn(warn_ets) | ||
| 465 | </pre></div></div> | ||
| 466 | </div> | ||
| 467 | <div·class="nboutput·docutils·container"> | ||
| 468 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: | ||
| 469 | </pre></div> | ||
| 470 | </div> | ||
| 471 | <div·class="output_area·docutils·container"> | ||
| 472 | <div·class="highlight"><pre> | ||
| 473 | <matplotlib.legend.Legend·at·0xadde5de1e8ed> | ||
| 474 | </pre></div></div> | ||
| 475 | </div> | ||
| 476 | <div·class="nboutput·docutils·container"> | ||
| 477 | <div·class="prompt·empty·docutils·container"> | ||
| 478 | </div> | ||
| 461 | <div·class="output_area·docutils·container"> | 479 | <div·class="output_area·docutils·container"> |
| 462 | <div·class="highlight"><pre> | 480 | <div·class="highlight"><pre> |
| 463 | RUNNING·THE·L-BFGS-B·CODE | 481 | RUNNING·THE·L-BFGS-B·CODE |
| 464 | ···········*·*·* | 482 | ···········*·*·* |
| 465 | Machine·precision·=·2.220D-16 | 483 | Machine·precision·=·2.220D-16 |
| Offset 139, 14 lines modified | Offset 139, 19 lines modified | ||
| 139 | #·obtained·from·R | 139 | #·obtained·from·R |
| 140 | params_R·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837, | 140 | params_R·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837, |
| 141 | 34.72584983] | 141 | 34.72584983] |
| 142 | yhat·=·model.smooth(params_R).fittedvalues | 142 | yhat·=·model.smooth(params_R).fittedvalues |
| 143 | yhat.plot(label="R·fit",·linestyle="--") | 143 | yhat.plot(label="R·fit",·linestyle="--") |
| 144 | plt.legend() | 144 | plt.legend() |
| 145 | /usr/lib/python3/dist-packages/statsmodels/tsa/exponential_smoothing/ets.py: | ||
| 146 | 437:·UserWarning:·ETSModel·can·give·wrong·results·on·32·bit·i386 | ||
| 147 | ··warnings.warn(warn_ets) | ||
| 148 | [4]: | ||
| 149 | <matplotlib.legend.Legend·at·0xadde5de1e8ed> | ||
| 145 | RUNNING·THE·L-BFGS-B·CODE | 150 | RUNNING·THE·L-BFGS-B·CODE |
| 146 | ···········*·*·* | 151 | ···········*·*·* |
| 147 | Machine·precision·=·2.220D-16 | 152 | Machine·precision·=·2.220D-16 |
| 148 | ·N·=············2·····M·=···········10 | 153 | ·N·=············2·····M·=···········10 |
| Offset 21, 18 lines modified | Offset 21, 18 lines modified | ||
| 21 | ············] | 21 | ············] |
| 22 | ········}, | 22 | ········}, |
| 23 | ········{ | 23 | ········{ |
| 24 | ············"cell_type":·"code", | 24 | ············"cell_type":·"code", |
| 25 | ············"execution_count":·1, | 25 | ············"execution_count":·1, |
| 26 | ············"metadata":·{ | 26 | ············"metadata":·{ |
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| 28 | ····················"iopub.execute_input":·"202 | 28 | ····················"iopub.execute_input":·"2025-05-17T08:05:26.483604Z", |
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| 32 | ················} | 32 | ················} |
| 33 | ············}, | 33 | ············}, |
| 34 | ············"outputs":·[], | 34 | ············"outputs":·[], |
| 35 | ············"source":·[ | 35 | ············"source":·[ |
| 36 | ················"import·numpy·as·np\n", | 36 | ················"import·numpy·as·np\n", |
| 37 | ················"import·matplotlib.pyplot·as·plt\n", | 37 | ················"import·matplotlib.pyplot·as·plt\n", |
| 38 | ················"import·pandas·as·pd\n", | 38 | ················"import·pandas·as·pd\n", |
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| 26 | ············"execution_count":·1, | 26 | ············"execution_count":·1, |
| 27 | ············"metadata":·{ | 27 | ············"metadata":·{ |
| 28 | ················"ExecuteTime":·{ | 28 | ················"ExecuteTime":·{ |
| 29 | ····················"end_time":·"2017-12-07T12:39:15.020317Z", | 29 | ····················"end_time":·"2017-12-07T12:39:15.020317Z", |
| 30 | ····················"start_time":·"2017-12-07T12:39:14.263100Z" | 30 | ····················"start_time":·"2017-12-07T12:39:14.263100Z" |
| 31 | ················}, | 31 | ················}, |
| 32 | ················"execution":·{ | 32 | ················"execution":·{ |
| 33 | ····················"iopub.execute_input":·"202 | 33 | ····················"iopub.execute_input":·"2025-05-17T08:05:24.691401Z", |
| 34 | ····················"iopub.status.busy":·"202 | 34 | ····················"iopub.status.busy":·"2025-05-17T08:05:24.690964Z", |
| 35 | ····················"iopub.status.idle":·"202 | 35 | ····················"iopub.status.idle":·"2025-05-17T08:05:27.142950Z", |
| 36 | ····················"shell.execute_reply":·"202 | 36 | ····················"shell.execute_reply":·"2025-05-17T08:05:27.141942Z" |
| 37 | ················} | 37 | ················} |
| 38 | ············}, | 38 | ············}, |
| 39 | ············"outputs":·[], | 39 | ············"outputs":·[], |
| 40 | ············"source":·[ | 40 | ············"source":·[ |
| 41 | ················"import·os\n", | 41 | ················"import·os\n", |
| 42 | ················"import·numpy·as·np\n", | 42 | ················"import·numpy·as·np\n", |
| 43 | ················"import·pandas·as·pd\n", | 43 | ················"import·pandas·as·pd\n", |
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| 19 | ············] | 19 | ············] |
| 20 | ········}, | 20 | ········}, |
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| 22 | ············"cell_type":·"code", | 22 | ············"cell_type":·"code", |
| 23 | ············"execution_count":·1, | 23 | ············"execution_count":·1, |
| 24 | ············"metadata":·{ | 24 | ············"metadata":·{ |
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| 31 | ················"jupyter":·{ | 31 | ················"jupyter":·{ |
| 32 | ····················"outputs_hidden":·false | 32 | ····················"outputs_hidden":·false |
| 33 | ················} | 33 | ················} |
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| 35 | ············"outputs":·[], | 35 | ············"outputs":·[], |
| 36 | ············"source":·[ | 36 | ············"source":·[ |
| 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> | 493 | ······<td>0.973595</td> |
| 494 | ····</tr> | 494 | ····</tr> |
| 495 | ····<tr> | 495 | ····<tr> |
| 496 | ······<th>level1_ix</th> | 496 | ······<th>level1_ix</th> |
| 497 | ······<td>1.97 | 497 | ······<td>1.976690</td> |
| 498 | ····</tr> | 498 | ····</tr> |
| 499 | ····<tr> | 499 | ····<tr> |
| 500 | ······<th>level2_ix</th> | 500 | ······<th>level2_ix</th> |
| 501 | ······<td> | 501 | ······<td>2.927767</td> |
| 502 | ····</tr> | 502 | ····</tr> |
| 503 | ····<tr> | 503 | ····<tr> |
| 504 | ······<th>Residual</th> | 504 | ······<th>Residual</th> |
| 505 | ······<td> | 505 | ······<td>3.977927</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 99, 18 lines modified | Offset 99, 18 lines modified | ||
| 99 | The·estimated·covariance·parameters·should·be·similar·to·groups_var, | 99 | The·estimated·covariance·parameters·should·be·similar·to·groups_var, |
| 100 | level1_var,·etc.·as·defined·above. | 100 | level1_var,·etc.·as·defined·above. |
| 101 | [13]: | 101 | [13]: |
| 102 | r.cov_struct.summary() | 102 | r.cov_struct.summary() |
| 103 | [13]: | 103 | [13]: |
| 104 | ·__________________ | 104 | ·__________________ |
| 105 | |_________|Variance| | 105 | |_________|Variance| |
| 106 | |groups_ix| | 106 | |groups_ix|0.973595| |
| 107 | |level1_ix|1.97 | 107 | |level1_ix|1.976690| |
| 108 | |level2_ix| | 108 | |level2_ix|2.927767| |
| 109 | |Residual_| | 109 | |Residual_|3.977927| |
| 110 | [Logo] | 110 | [Logo] |
| 111 | ****·Table_of_Contents·**** | 111 | ****·Table_of_Contents·**** |
| 112 | ····*·Installing_statsmodels | 112 | ····*·Installing_statsmodels |
| 113 | ····*·Getting_started | 113 | ····*·Getting_started |
| 114 | ····*·User_Guide | 114 | ····*·User_Guide |
| 115 | ····*·Examples | 115 | ····*·Examples |
| 116 | ····*·API_Reference | 116 | ····*·API_Reference |
| Offset 12, 18 lines modified | Offset 12, 18 lines modified | ||
| 12 | ············] | 12 | ············] |
| 13 | ········}, | 13 | ········}, |
| 14 | ········{ | 14 | ········{ |
| 15 | ············"cell_type":·"code", | 15 | ············"cell_type":·"code", |
| 16 | ············"execution_count":·1, | 16 | ············"execution_count":·1, |
| 17 | ············"metadata":·{ | 17 | ············"metadata":·{ |
| 18 | ················"execution":·{ | 18 | ················"execution":·{ |
| 19 | ····················"iopub.execute_input":·"202 | 19 | ····················"iopub.execute_input":·"2025-05-17T08:05:18.727316Z", |
| 20 | ····················"iopub.status.busy":·"202 | 20 | ····················"iopub.status.busy":·"2025-05-17T08:05:18.726886Z", |
| 21 | ····················"iopub.status.idle":·"202 | 21 | ····················"iopub.status.idle":·"2025-05-17T08:05:20.320722Z", |
| 22 | ····················"shell.execute_reply":·"202 | 22 | ····················"shell.execute_reply":·"2025-05-17T08:05:20.305337Z" |
| 23 | ················} | 23 | ················} |
| 24 | ············}, | 24 | ············}, |
| 25 | ············"outputs":·[], | 25 | ············"outputs":·[], |
| 26 | ············"source":·[ | 26 | ············"source":·[ |
| 27 | ················"import·numpy·as·np\n", | 27 | ················"import·numpy·as·np\n", |
| 28 | ················"import·pandas·as·pd\n", | 28 | ················"import·pandas·as·pd\n", |
| 29 | ················"import·statsmodels.api·as·sm" | 29 | ················"import·statsmodels.api·as·sm" |
| Offset 14, 18 lines modified | Offset 14, 18 lines modified | ||
| 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":·"202 | 21 | ····················"iopub.execute_input":·"2025-05-17T08:05:11.028349Z", |
| 22 | ····················"iopub.status.busy":·"202 | 22 | ····················"iopub.status.busy":·"2025-05-17T08:05:11.027972Z", |
| 23 | ····················"iopub.status.idle":·"202 | 23 | ····················"iopub.status.idle":·"2025-05-17T08:05:13.661978Z", |
| 24 | ····················"shell.execute_reply":·"202 | 24 | ····················"shell.execute_reply":·"2025-05-17T08:05:13.645954Z" |
| 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 27, 18 lines modified | Offset 27, 18 lines modified | ||
| 27 | ············] | 27 | ············] |
| 28 | ········}, | 28 | ········}, |
| 29 | ········{ | 29 | ········{ |
| 30 | ············"cell_type":·"code", | 30 | ············"cell_type":·"code", |
| 31 | ············"execution_count":·1, | 31 | ············"execution_count":·1, |
| 32 | ············"metadata":·{ | 32 | ············"metadata":·{ |
| 33 | ················"execution":·{ | 33 | ················"execution":·{ |
| 34 | ····················"iopub.execute_input":·"202 | 34 | ····················"iopub.execute_input":·"2025-05-17T08:05:10.975150Z", |
| 35 | ····················"iopub.status.busy":·"202 | 35 | ····················"iopub.status.busy":·"2025-05-17T08:05:10.974743Z", |
| 36 | ····················"iopub.status.idle":·"202 | 36 | ····················"iopub.status.idle":·"2025-05-17T08:05:12.338529Z", |
| 37 | ····················"shell.execute_reply":·"202 | 37 | ····················"shell.execute_reply":·"2025-05-17T08:05:12.325959Z" |
| 38 | ················}, | 38 | ················}, |
| 39 | ················"jupyter":·{ | 39 | ················"jupyter":·{ |
| 40 | ····················"outputs_hidden":·false | 40 | ····················"outputs_hidden":·false |
| 41 | ················} | 41 | ················} |
| 42 | ············}, | 42 | ············}, |
| 43 | ············"outputs":·[], | 43 | ············"outputs":·[], |
| 44 | ············"source":·[ | 44 | ············"source":·[ |
| Offset 631, 15 lines modified | Offset 631, 15 lines modified | ||
| 631 | </pre></div></div> | 631 | </pre></div></div> |
| 632 | </div> | 632 | </div> |
| 633 | <div·class="nboutput·nblast·docutils·container"> | 633 | <div·class="nboutput·nblast·docutils·container"> |
| 634 | <div·class="prompt·empty·docutils·container"> | 634 | <div·class="prompt·empty·docutils·container"> |
| 635 | </div> | 635 | </div> |
| 636 | <div·class="output_area·stderr·docutils·container"> | 636 | <div·class="output_area·stderr·docutils·container"> |
| 637 | <div·class="highlight"><pre> | 637 | <div·class="highlight"><pre> |
| 638 | /tmp/ipykernel_ | 638 | /tmp/ipykernel_3606/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use·float(ser.iloc[0])·instead |
| 639 | ··print("%2.4f%%"·%·(diff*100)) | 639 | ··print("%2.4f%%"·%·(diff*100)) |
| 640 | </pre></div></div> | 640 | </pre></div></div> |
| 641 | </div> | 641 | </div> |
| 642 | </section> | 642 | </section> |
| 643 | <section·id="Plots"> | 643 | <section·id="Plots"> |
| 644 | <h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3> | 644 | <h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3> |
| 645 | <p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p> | 645 | <p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p> |
| Offset 266, 15 lines modified | Offset 266, 15 lines modified | ||
| 266 | resp_75·=·res.predict(means75) | 266 | resp_75·=·res.predict(means75) |
| 267 | diff·=·resp_75·-·resp_25 | 267 | diff·=·resp_75·-·resp_25 |
| 268 | The·interquartile·first·difference·for·the·percentage·of·low·income·households | 268 | The·interquartile·first·difference·for·the·percentage·of·low·income·households |
| 269 | in·a·school·district·is: | 269 | in·a·school·district·is: |
| 270 | [10]: | 270 | [10]: |
| 271 | print("%2.4f%%"·%·(diff*100)) | 271 | print("%2.4f%%"·%·(diff*100)) |
| 272 | -11.8753% | 272 | -11.8753% |
| 273 | /tmp/ipykernel_ | 273 | /tmp/ipykernel_3606/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single |
| 274 | element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use | 274 | element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use |
| 275 | float(ser.iloc[0])·instead | 275 | float(ser.iloc[0])·instead |
| 276 | ··print("%2.4f%%"·%·(diff*100)) | 276 | ··print("%2.4f%%"·%·(diff*100)) |
| 277 | ****·Plots¶·**** | 277 | ****·Plots¶·**** |
| 278 | We·extract·information·that·will·be·used·to·draw·some·interesting·plots: | 278 | We·extract·information·that·will·be·used·to·draw·some·interesting·plots: |
| 279 | [11]: | 279 | [11]: |
| Offset 8, 34 lines modified | Offset 8, 34 lines modified | ||
| 8 | ············] | 8 | ············] |
| 9 | ········}, | 9 | ········}, |
| 10 | ········{ | 10 | ········{ |
| 11 | ············"cell_type":·"code", | 11 | ············"cell_type":·"code", |
| 12 | ············"execution_count":·1, | 12 | ············"execution_count":·1, |
| 13 | ············"metadata":·{ | 13 | ············"metadata":·{ |
| 14 | ················"execution":·{ | 14 | ················"execution":·{ |
| 15 | ····················"iopub.execute_input":·"202 | 15 | ····················"iopub.execute_input":·"2025-05-17T08:05:11.287358Z", |
| 16 | ····················"iopub.status.busy":·"202 | 16 | ····················"iopub.status.busy":·"2025-05-17T08:05:11.286904Z", |
| 17 | ····················"iopub.status.idle":·"202 | 17 | ····················"iopub.status.idle":·"2025-05-17T08:05:12.118321Z", |
| 18 | ····················"shell.execute_reply":·"202 | 18 | ····················"shell.execute_reply":·"2025-05-17T08:05:12.106925Z" |
| 19 | ················} | 19 | ················} |
| 20 | ············}, | 20 | ············}, |
| 21 | ············"outputs":·[], | 21 | ············"outputs":·[], |
| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"%matplotlib·inline" | 23 | ················"%matplotlib·inline" |
| 24 | ············] | 24 | ············] |
| 25 | ········}, | 25 | ········}, |
| 26 | ········{ | 26 | ········{ |
| 27 | ············"cell_type":·"code", | 27 | ············"cell_type":·"code", |
| 28 | ············"execution_count":·2, | 28 | ············"execution_count":·2, |
| 29 | ············"metadata":·{ | 29 | ············"metadata":·{ |
| 30 | ················"execution":·{ | 30 | ················"execution":·{ |
| 31 | ····················"iopub.execute_input":·"202 | 31 | ····················"iopub.execute_input":·"2025-05-17T08:05:12.139531Z", |
| 32 | ····················"iopub.status.busy":·"202 | 32 | ····················"iopub.status.busy":·"2025-05-17T08:05:12.139029Z", |
| 33 | ····················"iopub.status.idle":·"202 | 33 | ····················"iopub.status.idle":·"2025-05-17T08:05:13.969977Z", |
| 34 | ····················"shell.execute_reply":·"202 | 34 | ····················"shell.execute_reply":·"2025-05-17T08:05:13.955193Z" |
| 35 | ················} | 35 | ················} |
| 36 | ············}, | 36 | ············}, |
| 37 | ············"outputs":·[], | 37 | ············"outputs":·[], |
| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"import·numpy·as·np\n", | 39 | ················"import·numpy·as·np\n", |
| 40 | ················"import·statsmodels.api·as·sm\n", | 40 | ················"import·statsmodels.api·as·sm\n", |
| 41 | ················"from·scipy·import·stats\n", | 41 | ················"from·scipy·import·stats\n", |
| 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_ | 493 | /tmp/ipykernel_3608/1000445862.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_ | 495 | /tmp/ipykernel_3608/1000445862.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 196, 23 lines modified | Offset 196, 23 lines modified | ||
| 196 | As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half | 196 | As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half |
| 197 | the·size·of·the·LOWINC·coefficient·from·the·first·model: | 197 | the·size·of·the·LOWINC·coefficient·from·the·first·model: |
| 198 | [4]: | 198 | [4]: |
| 199 | print(mod1.params[1]) | 199 | print(mod1.params[1]) |
| 200 | print(mod2.params[1]·*·2) | 200 | print(mod2.params[1]·*·2) |
| 201 | -0.020395987154755834 | 201 | -0.020395987154755834 |
| 202 | -0.020395987154756382 | 202 | -0.020395987154756382 |
| 203 | /tmp/ipykernel_ | 203 | /tmp/ipykernel_3608/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating |
| 204 | 204 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always | |
| 205 | 205 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by | |
| 206 | 206 | position,·use·`ser.iloc[pos]` | |
| 207 | ··print(mod1.params[1]) | 207 | ··print(mod1.params[1]) |
| 208 | /tmp/ipykernel_ | 208 | /tmp/ipykernel_3608/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating |
| 209 | 209 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always | |
| 210 | 210 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by | |
| 211 | 211 | position,·use·`ser.iloc[pos]` | |
| 212 | ··print(mod2.params[1]·*·2) | 212 | ··print(mod2.params[1]·*·2) |
| 213 | [Logo] | 213 | [Logo] |
| 214 | ****·Table_of_Contents·**** | 214 | ****·Table_of_Contents·**** |
| 215 | ····*·Installing_statsmodels | 215 | ····*·Installing_statsmodels |
| 216 | ····*·Getting_started | 216 | ····*·Getting_started |
| 217 | ····*·User_Guide | 217 | ····*·User_Guide |
| 218 | ····*·Examples | 218 | ····*·Examples |
| Offset 17, 18 lines modified | Offset 17, 18 lines modified | ||
| 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":·{ |
| 23 | ················"execution":·{ | 23 | ················"execution":·{ |
| 24 | ····················"iopub.execute_input":·"202 | 24 | ····················"iopub.execute_input":·"2025-05-17T08:05:11.307319Z", |
| 25 | ····················"iopub.status.busy":·"202 | 25 | ····················"iopub.status.busy":·"2025-05-17T08:05:11.306896Z", |
| 26 | ····················"iopub.status.idle":·"202 | 26 | ····················"iopub.status.idle":·"2025-05-17T08:05:13.022538Z", |
| 27 | ····················"shell.execute_reply":·"202 | 27 | ····················"shell.execute_reply":·"2025-05-17T08:05:13.021533Z" |
| 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":·[ |
| Offset 8, 18 lines modified | Offset 8, 18 lines modified | ||
| 8 | ············] | 8 | ············] |
| 9 | ········}, | 9 | ········}, |
| 10 | ········{ | 10 | ········{ |
| 11 | ············"cell_type":·"code", | 11 | ············"cell_type":·"code", |
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| 15 | ····················"iopub.execute_input":·"202 | 15 | ····················"iopub.execute_input":·"2025-05-17T08:05:27.723447Z", |
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| 19 | ················} | 19 | ················} |
| 20 | ············}, | 20 | ············}, |
| 21 | ············"outputs":·[], | 21 | ············"outputs":·[], |
| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"import·numpy·as·np\n", | 23 | ················"import·numpy·as·np\n", |
| 24 | ················"import·pandas·as·pd\n", | 24 | ················"import·pandas·as·pd\n", |
| 25 | ················"import·statsmodels.formula.api·as·smf\n", | 25 | ················"import·statsmodels.formula.api·as·smf\n", |
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| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"%matplotlib·inline\n", | 39 | ················"%matplotlib·inline\n", |
| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
| 41 | ················"from·scipy·import·stats\n", | 41 | ················"from·scipy·import·stats\n", |
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| 17 | ············"metadata":·{ | 17 | ············"metadata":·{ |
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| 19 | ····················"iopub.execute_input":·"202 | 19 | ····················"iopub.execute_input":·"2025-05-17T08:05:10.831464Z", |
| 20 | ····················"iopub.status.busy":·"202 | 20 | ····················"iopub.status.busy":·"2025-05-17T08:05:10.830822Z", |
| 21 | ····················"iopub.status.idle":·"202 | 21 | ····················"iopub.status.idle":·"2025-05-17T08:05:14.049976Z", |
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| 23 | ················} | 23 | ················} |
| 24 | ············}, | 24 | ············}, |
| 25 | ············"outputs":·[], | 25 | ············"outputs":·[], |
| 26 | ············"source":·[ | 26 | ············"source":·[ |
| 27 | ················"import·numpy·as·np\n", | 27 | ················"import·numpy·as·np\n", |
| 28 | ················"import·pylab\n", | 28 | ················"import·pylab\n", |
| 29 | ················"import·seaborn·as·sns\n", | 29 | ················"import·seaborn·as·sns\n", |
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| 27 | ····················"iopub.status.idle":·"202 | 27 | ····················"iopub.status.idle":·"2025-05-17T08:05:18.985400Z", |
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| 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", |
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| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"%matplotlib·inline" | 39 | ················"%matplotlib·inline" |
| 40 | ············] | 40 | ············] |
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| 48 | ····················"iopub.status.busy":·"202 | 48 | ····················"iopub.status.busy":·"2025-05-17T08:05:18.325411Z", |
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| 50 | ····················"shell.execute_reply":·"202 | 50 | ····················"shell.execute_reply":·"2025-05-17T08:05:19.336607Z" |
| 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 705, 23 lines modified | Offset 705, 14 lines modified | ||
| 705 | <span·class="nb">print</span><span·class="p">(</span><span·class="n">mdf</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span> | 705 | <span·class="nb">print</span><span·class="p">(</span><span·class="n">mdf</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span> |
| 706 | </pre></div> | 706 | </pre></div> |
| 707 | </div> | 707 | </div> |
| 708 | </div> | 708 | </div> |
| 709 | <div·class="nboutput·docutils·container"> | 709 | <div·class="nboutput·docutils·container"> |
| 710 | <div·class="prompt·empty·docutils·container"> | 710 | <div·class="prompt·empty·docutils·container"> |
| 711 | </div> | 711 | </div> |
| 712 | <div·class="output_area·stderr·docutils·container"> | ||
| 713 | <div·class="highlight"><pre> | ||
| 714 | /usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:2238:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter·space. | ||
| 715 | ··warnings.warn(msg,·ConvergenceWarning) | ||
| 716 | </pre></div></div> | ||
| 717 | </div> | ||
| 718 | <div·class="nboutput·nblast·docutils·container"> | ||
| 719 | <div·class="prompt·empty·docutils·container"> | ||
| 720 | </div> | ||
| 721 | <div·class="output_area·docutils·container"> | 712 | <div·class="output_area·docutils·container"> |
| 722 | <div·class="highlight"><pre> | 713 | <div·class="highlight"><pre> |
| 723 | ·············Mixed·Linear·Model·Regression·Results | 714 | ·············Mixed·Linear·Model·Regression·Results |
| 724 | =============================================================== | 715 | =============================================================== |
| 725 | Model:···············MixedLM····Dependent·Variable:····size | 716 | Model:···············MixedLM····Dependent·Variable:····size |
| 726 | No.·Observations:····395········Method:················REML | 717 | No.·Observations:····395········Method:················REML |
| 727 | No.·Groups:··········79·········Scale:·················0.0264 | 718 | No.·Groups:··········79·········Scale:·················0.0264 |
| Offset 338, 18 lines modified | Offset 338, 14 lines modified | ||
| 338 | being·on·the·boundary·of·the·parameter·space.·The·regression·slopes·agree·very | 338 | being·on·the·boundary·of·the·parameter·space.·The·regression·slopes·agree·very |
| 339 | well·with·R,·but·the·likelihood·value·is·much·higher·than·that·returned·by·R. | 339 | well·with·R,·but·the·likelihood·value·is·much·higher·than·that·returned·by·R. |
| 340 | [8]: | 340 | [8]: |
| 341 | exog_re·=·exog.copy() | 341 | exog_re·=·exog.copy() |
| 342 | md·=·sm.MixedLM(endog,·exog,·data["tree"],·exog_re) | 342 | md·=·sm.MixedLM(endog,·exog,·data["tree"],·exog_re) |
| 343 | mdf·=·md.fit() | 343 | mdf·=·md.fit() |
| 344 | print(mdf.summary()) | 344 | print(mdf.summary()) |
| 345 | /usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py: | ||
| 346 | 2238:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter | ||
| 347 | space. | ||
| 348 | ··warnings.warn(msg,·ConvergenceWarning) | ||
| 349 | ·············Mixed·Linear·Model·Regression·Results | 345 | ·············Mixed·Linear·Model·Regression·Results |
| 350 | =============================================================== | 346 | =============================================================== |
| 351 | Model:···············MixedLM····Dependent·Variable:····size | 347 | Model:···············MixedLM····Dependent·Variable:····size |
| 352 | No.·Observations:····395········Method:················REML | 348 | No.·Observations:····395········Method:················REML |
| 353 | No.·Groups:··········79·········Scale:·················0.0264 | 349 | No.·Groups:··········79·········Scale:·················0.0264 |
| 354 | Min.·group·size:·····5··········Log-Likelihood:········-62.4834 | 350 | Min.·group·size:·····5··········Log-Likelihood:········-62.4834 |
| 355 | Max.·group·size:·····5··········Converged:·············Yes | 351 | Max.·group·size:·····5··········Converged:·············Yes |
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| 8 | ············] | 8 | ············] |
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| 8 | ············] | 8 | ············] |
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| 23 | ················"%matplotlib·inline" | 23 | ················"%matplotlib·inline" |
| 24 | ············] | 24 | ············] |
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| 39 | ················"import·matplotlib.pyplot·as·plt\n", | 39 | ················"import·matplotlib.pyplot·as·plt\n", |
| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
| 41 | ················"import·pandas·as·pd\n", | 41 | ················"import·pandas·as·pd\n", |
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| 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_4 | 806 | /tmp/ipykernel_4315/427128218.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 147, 15 lines modified | Offset 147, 15 lines modified | ||
| 147 | lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6) | 147 | lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6) |
| 148 | ax.set_xticklabels(dta.columns.values[::10]) | 148 | ax.set_xticklabels(dta.columns.values[::10]) |
| 149 | ax.set_xlim(0,·51) | 149 | ax.set_xlim(0,·51) |
| 150 | ax.set_xlabel("Year",·size=17) | 150 | ax.set_xlabel("Year",·size=17) |
| 151 | fig.subplots_adjust(0.1,·0.1,·0.85,·0.9) | 151 | fig.subplots_adjust(0.1,·0.1,·0.85,·0.9) |
| 152 | legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right") | 152 | legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right") |
| 153 | legend.draw_frame(False) | 153 | legend.draw_frame(False) |
| 154 | /tmp/ipykernel_4 | 154 | /tmp/ipykernel_4315/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be |
| 155 | used·together·with·FixedLocator | 155 | used·together·with·FixedLocator |
| 156 | ··ax.set_xticklabels(dta.columns.values[::10]) | 156 | ··ax.set_xticklabels(dta.columns.values[::10]) |
| 157 | [../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png] | 157 | [../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png] |
| 158 | To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories | 158 | To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories |
| 159 | for·sets·of·countries·with·similar·PC·scores.·The·following·convenience | 159 | for·sets·of·countries·with·similar·PC·scores.·The·following·convenience |
| 160 | function·produces·such·a·plot. | 160 | function·produces·such·a·plot. |
| 161 | [8]: | 161 | [8]: |
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| 17 | ············] | 17 | ············] |
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| 58 | ················"import·pandas·as·pd\n", | 58 | ················"import·pandas·as·pd\n", |
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| 41 | ················"import·matplotlib.pyplot·as·plt\n", | 41 | ················"import·matplotlib.pyplot·as·plt\n", |
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| 39 | ················"import·matplotlib.pyplot·as·plt\n", | 39 | ················"import·matplotlib.pyplot·as·plt\n", |
| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
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| 2055 | </div> | 2055 | </div> |
| 2056 | <div·class="nboutput·nblast·docutils·container"> | 2056 | <div·class="nboutput·nblast·docutils·container"> |
| 2057 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[67]: | 2057 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[67]: |
| 2058 | </pre></div> | 2058 | </pre></div> |
| 2059 | </div> | 2059 | </div> |
| 2060 | <div·class="output_area·docutils·container"> | 2060 | <div·class="output_area·docutils·container"> |
| 2061 | <div·class="highlight"><pre> | 2061 | <div·class="highlight"><pre> |
| 2062 | 0.445029487306832 | 2062 | 0.4450294873068329 |
| 2063 | </pre></div></div> | 2063 | </pre></div></div> |
| 2064 | </div> | 2064 | </div> |
| 2065 | <div·class="nbinput·docutils·container"> | 2065 | <div·class="nbinput·docutils·container"> |
| 2066 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[68]: | 2066 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[68]: |
| 2067 | </pre></div> | 2067 | </pre></div> |
| 2068 | </div> | 2068 | </div> |
| 2069 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">all_betas</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">)</span> | 2069 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">all_betas</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">)</span> |
| Offset 921, 15 lines modified | Offset 921, 15 lines modified | ||
| 921 | all_betas·=·np.asarray(all_betas) | 921 | all_betas·=·np.asarray(all_betas) |
| 922 | se_loss·=·lambda·x:·np.linalg.norm(x,·ord=2)·**·2 | 922 | se_loss·=·lambda·x:·np.linalg.norm(x,·ord=2)·**·2 |
| 923 | se_beta·=·lmap(se_loss,·all_betas·-·beta_true) | 923 | se_beta·=·lmap(se_loss,·all_betas·-·beta_true) |
| 924 | ****·Squared·error·loss¶·**** | 924 | ****·Squared·error·loss¶·**** |
| 925 | [67]: | 925 | [67]: |
| 926 | np.array(se_beta).mean() | 926 | np.array(se_beta).mean() |
| 927 | [67]: | 927 | [67]: |
| 928 | 0.445029487306832 | 928 | 0.4450294873068329 |
| 929 | [68]: | 929 | [68]: |
| 930 | all_betas.mean(0) | 930 | all_betas.mean(0) |
| 931 | [68]: | 931 | [68]: |
| 932 | array([·2.99711706,··0.99898147,··2.49909344,··2.99712918,·-3.99626521]) | 932 | array([·2.99711706,··0.99898147,··2.49909344,··2.99712918,·-3.99626521]) |
| 933 | [69]: | 933 | [69]: |
| 934 | beta_true | 934 | beta_true |
| 935 | [69]: | 935 | [69]: |
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| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
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| 24 | ····················"iopub.status.busy":·"202 | 24 | ····················"iopub.status.busy":·"2025-05-17T08:05:25.778873Z", |
| 25 | ····················"iopub.status.idle":·"202 | 25 | ····················"iopub.status.idle":·"2025-05-17T08:05:26.542327Z", |
| 26 | ····················"shell.execute_reply":·"202 | 26 | ····················"shell.execute_reply":·"2025-05-17T08:05:26.534986Z" |
| 27 | ················}, | 27 | ················}, |
| 28 | ················"jupyter":·{ | 28 | ················"jupyter":·{ |
| 29 | ····················"outputs_hidden":·false | 29 | ····················"outputs_hidden":·false |
| 30 | ················} | 30 | ················} |
| 31 | ············}, | 31 | ············}, |
| 32 | ············"outputs":·[], | 32 | ············"outputs":·[], |
| 33 | ············"source":·[ | 33 | ············"source":·[ |
| 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_4 | 585 | /tmp/ipykernel_4950/976557282.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_4 | 587 | /tmp/ipykernel_4950/976557282.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_4 | 589 | /tmp/ipykernel_4950/976557282.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 265, 25 lines modified | Offset 265, 25 lines modified | ||
| 265 | Original·model | 265 | Original·model |
| 266 | var.level·····=·0.74469 | 266 | var.level·····=·0.74469 |
| 267 | var.irregular·=·3.37330 | 267 | var.irregular·=·3.37330 |
| 268 | Concentrated·model | 268 | Concentrated·model |
| 269 | scale·········=·0.74472 | 269 | scale·········=·0.74472 |
| 270 | h·*·scale·····=·3.37338 | 270 | h·*·scale·····=·3.37338 |
| 271 | /tmp/ipykernel_4 | 271 | /tmp/ipykernel_4950/976557282.py:2:·FutureWarning:·Series.__getitem__·treating |
| 272 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always | 272 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always |
| 273 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by | 273 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by |
| 274 | position,·use·`ser.iloc[pos]` | 274 | position,·use·`ser.iloc[pos]` |
| 275 | ··print('var.level·····=·%.5f'·%·res.params[0]) | 275 | ··print('var.level·····=·%.5f'·%·res.params[0]) |
| 276 | /tmp/ipykernel_4 | 276 | /tmp/ipykernel_4950/976557282.py:3:·FutureWarning:·Series.__getitem__·treating |
| 277 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always | 277 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always |
| 278 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by | 278 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by |
| 279 | position,·use·`ser.iloc[pos]` | 279 | position,·use·`ser.iloc[pos]` |
| 280 | ··print('var.irregular·=·%.5f'·%·res.params[1]) | 280 | ··print('var.irregular·=·%.5f'·%·res.params[1]) |
| 281 | /tmp/ipykernel_4 | 281 | /tmp/ipykernel_4950/976557282.py:7:·FutureWarning:·Series.__getitem__·treating |
| 282 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always | 282 | keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always |
| 283 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by | 283 | be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by |
| 284 | position,·use·`ser.iloc[pos]` | 284 | position,·use·`ser.iloc[pos]` |
| 285 | ··print('h·*·scale·····=·%.5f'·%·(res_conc.params[0]·*·res_conc.scale)) | 285 | ··print('h·*·scale·····=·%.5f'·%·(res_conc.params[0]·*·res_conc.scale)) |
| 286 | *****·Example:·SARIMAX¶·***** | 286 | *****·Example:·SARIMAX¶·***** |
| 287 | By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically | 287 | By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically |
| Offset 8, 18 lines modified | Offset 8, 18 lines modified | ||
| 8 | ············] | 8 | ············] |
| 9 | ········}, | 9 | ········}, |
| 10 | ········{ | 10 | ········{ |
| 11 | ············"cell_type":·"code", | 11 | ············"cell_type":·"code", |
| 12 | ············"execution_count":·1, | 12 | ············"execution_count":·1, |
| 13 | ············"metadata":·{ | 13 | ············"metadata":·{ |
| 14 | ················"execution":·{ | 14 | ················"execution":·{ |
| 15 | ····················"iopub.execute_input":·"202 | 15 | ····················"iopub.execute_input":·"2025-05-17T08:05:27.267457Z", |
| 16 | ····················"iopub.status.busy":·"202 | 16 | ····················"iopub.status.busy":·"2025-05-17T08:05:27.266982Z", |
| 17 | ····················"iopub.status.idle":·"202 | 17 | ····················"iopub.status.idle":·"2025-05-17T08:05:28.957550Z", |
| 18 | ····················"shell.execute_reply":·"202 | 18 | ····················"shell.execute_reply":·"2025-05-17T08:05:28.956535Z" |
| 19 | ················} | 19 | ················} |
| 20 | ············}, | 20 | ············}, |
| 21 | ············"outputs":·[], | 21 | ············"outputs":·[], |
| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"import·numpy·as·np\n", | 23 | ················"import·numpy·as·np\n", |
| 24 | ················"import·pandas·as·pd\n", | 24 | ················"import·pandas·as·pd\n", |
| 25 | ················"import·statsmodels.api·as·sm\n", | 25 | ················"import·statsmodels.api·as·sm\n", |
| Offset 17, 18 lines modified | Offset 17, 18 lines modified | ||
| 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":·{ |
| 23 | ················"execution":·{ | 23 | ················"execution":·{ |
| 24 | ····················"iopub.execute_input":·"202 | 24 | ····················"iopub.execute_input":·"2025-05-17T08:05:17.939292Z", |
| 25 | ····················"iopub.status.busy":·"202 | 25 | ····················"iopub.status.busy":·"2025-05-17T08:05:17.938848Z", |
| 26 | ····················"iopub.status.idle":·"202 | 26 | ····················"iopub.status.idle":·"2025-05-17T08:05:20.630005Z", |
| 27 | ····················"shell.execute_reply":·"202 | 27 | ····················"shell.execute_reply":·"2025-05-17T08:05:20.618985Z" |
| 28 | ················} | 28 | ················} |
| 29 | ············}, | 29 | ············}, |
| 30 | ············"outputs":·[], | 30 | ············"outputs":·[], |
| 31 | ············"source":·[ | 31 | ············"source":·[ |
| 32 | ················"%matplotlib·inline\n", | 32 | ················"%matplotlib·inline\n", |
| 33 | ················"\n", | 33 | ················"\n", |
| 34 | ················"import·numpy·as·np\n", | 34 | ················"import·numpy·as·np\n", |
| Offset 339, 23 lines modified | Offset 339, 23 lines modified | ||
| 339 | \[\begin{split}\begin{align} | 339 | \[\begin{split}\begin{align} |
| 340 | Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\ | 340 | Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\ |
| 341 | \eta_t·&·\sim·WN(0,\sigma^2)·\\ | 341 | \eta_t·&·\sim·WN(0,\sigma^2)·\\ |
| 342 | \end{align}\end{split}\]</div> | 342 | \end{align}\end{split}\]</div> |
| 343 | <p>This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using·OLS·(<code·class="docutils·literal·notranslate"><span·class="pre">AutoReg</span></code>).·In·large·samples,·<span·class="math·notranslate·nohighlight">\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-\rho)\)</span>.</p> | 343 | <p>This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using·OLS·(<code·class="docutils·literal·notranslate"><span·class="pre">AutoReg</span></code>).·In·large·samples,·<span·class="math·notranslate·nohighlight">\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-\rho)\)</span>.</p> |
| 344 | <p>In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship·hold·in·practice.</p> | 344 | <p>In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship·hold·in·practice.</p> |
| 345 | <div·class="nbinput·nblast·docutils·container"> | 345 | <div·class="nbinput·nblast·docutils·container"> |
| 346 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[ | 346 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]: |
| 347 | </pre></div> | 347 | </pre></div> |
| 348 | </div> | 348 | </div> |
| 349 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline | 349 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline |
| 350 | </pre></div> | 350 | </pre></div> |
| 351 | </div> | 351 | </div> |
| 352 | </div> | 352 | </div> |
| 353 | <div·class="nbinput·nblast·docutils·container"> | 353 | <div·class="nbinput·nblast·docutils·container"> |
| 354 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[ | 354 | <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: |
| 355 | </pre></div> | 355 | </pre></div> |
| 356 | </div> | 356 | </div> |
| 357 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span> | 357 | <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span> |
| 358 | <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span> | 358 | <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span> |
| 359 | <span·class="n">rng</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">default_rng</span><span·class="p">(</span><span·class="mi">20210819</span><span·class="p">)</span> | 359 | <span·class="n">rng</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">default_rng</span><span·class="p">(</span><span·class="mi">20210819</span><span·class="p">)</span> |
| 360 | <span·class="n">eta</span>·<span·class="o">=</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">5200</span><span·class="p">)</span> | 360 | <span·class="n">eta</span>·<span·class="o">=</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">5200</span><span·class="p">)</span> |
| Offset 45, 44 lines modified | Offset 45, 102 lines modified | ||
| 45 | \[\begin{split}\begin{align}·Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\·\eta_t·& | 45 | \[\begin{split}\begin{align}·Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\·\eta_t·& |
| 46 | \sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\] | 46 | \sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\] |
| 47 | This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using | 47 | This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using |
| 48 | OLS·(AutoReg).·In·large·samples,·\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1- | 48 | OLS·(AutoReg).·In·large·samples,·\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1- |
| 49 | \rho)\). | 49 | \rho)\). |
| 50 | In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship | 50 | In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship |
| 51 | hold·in·practice. | 51 | hold·in·practice. |
| 52 | [ | 52 | [1]: |
| 53 | %matplotlib·inline | 53 | %matplotlib·inline |
| 54 | [ | 54 | [2]: |
| 55 | import·numpy·as·np | 55 | import·numpy·as·np |
| 56 | import·pandas·as·pd | 56 | import·pandas·as·pd |
| 57 | rng·=·np.random.default_rng(20210819) | 57 | rng·=·np.random.default_rng(20210819) |
| 58 | eta·=·rng.standard_normal(5200) | 58 | eta·=·rng.standard_normal(5200) |
| 59 | rho·=·0.8 | 59 | rho·=·0.8 |
| 60 | beta·=·10 | 60 | beta·=·10 |
| 61 | epsilon·=·eta.copy() | 61 | epsilon·=·eta.copy() |
| 62 | for·i·in·range(1,·eta.shape[0]): | 62 | for·i·in·range(1,·eta.shape[0]): |
| 63 | ····epsilon[i]·=·rho·*·epsilon[i·-·1]·+·eta[i] | 63 | ····epsilon[i]·=·rho·*·epsilon[i·-·1]·+·eta[i] |
| 64 | y·=·beta·+·epsilon | 64 | y·=·beta·+·epsilon |
| 65 | y·=·y[200:] | 65 | y·=·y[200:] |
| 66 | [ | 66 | [3]: |
| 67 | from·statsmodels.tsa.api·import·SARIMAX,·AutoReg | 67 | from·statsmodels.tsa.api·import·SARIMAX,·AutoReg |
| 68 | from·statsmodels.tsa.arima.model·import·ARIMA | 68 | from·statsmodels.tsa.arima.model·import·ARIMA |
| 69 | The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is | 69 | The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is |
| 70 | included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators. | 70 | included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators. |
| 71 | [ | 71 | [4]: |
| 72 | ar0_res·=·SARIMAX(y,·order=(0,·0,·0),·trend="c").fit() | 72 | ar0_res·=·SARIMAX(y,·order=(0,·0,·0),·trend="c").fit() |
| 73 | sarimax_res·=·SARIMAX(y,·order=(1,·0,·0),·trend="c").fit() | 73 | sarimax_res·=·SARIMAX(y,·order=(1,·0,·0),·trend="c").fit() |
| 74 | arima_res·=·ARIMA(y,·order=(1,·0,·0),·trend="c").fit() | 74 | arima_res·=·ARIMA(y,·order=(1,·0,·0),·trend="c").fit() |
| 75 | autoreg_res·=·AutoReg(y,·1,·trend="c").fit() | 75 | autoreg_res·=·AutoReg(y,·1,·trend="c").fit() |
| 76 | RUNNING·THE·L-BFGS-B·CODE | ||
| 77 | ···········*·*·* | ||
| 78 | Machine·precision·=·2.220D-16 | ||
| 79 | ·N·=············2·····M·=···········10 | ||
| 80 | ·This·problem·is·unconstrained. | ||
| 81 | At·X0·········0·variables·are·exactly·at·the·bounds | ||
| 82 | At·iterate····0····f=··1.91760D+00····|proj·g|=··3.68860D-06 | ||
| 83 | ···········*·*·* | ||
| 84 | Tit···=·total·number·of·iterations | ||
| 85 | Tnf···=·total·number·of·function·evaluations | ||
| 86 | Tnint·=·total·number·of·segments·explored·during·Cauchy·searches | ||
| 87 | Skip··=·number·of·BFGS·updates·skipped | ||
| 88 | Nact··=·number·of·active·bounds·at·final·generalized·Cauchy·point | ||
| 89 | Projg·=·norm·of·the·final·projected·gradient | ||
| 90 | F·····=·final·function·value | ||
| 91 | ···········*·*·* | ||
| 92 | ···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F | ||
| 93 | ····2······0······1······0·····0·····0···3.689D-06···1.918D+00 | ||
| 94 | ··F·=···1.9175996129577773 | ||
| 95 | CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL | ||
| 96 | RUNNING·THE·L-BFGS-B·CODE | ||
| 97 | ···········*·*·* | ||
| 98 | Machine·precision·=·2.220D-16 | ||
| 99 | ·N·=············3·····M·=···········10 | ||
| 100 | ·This·problem·is·unconstrained. | ||
| 101 | At·X0·········0·variables·are·exactly·at·the·bounds | ||
| 102 | At·iterate····0····f=··1.41373D+00····|proj·g|=··9.51828D-04 | ||
| 103 | ···········*·*·* | ||
| 104 | Tit···=·total·number·of·iterations | ||
| 105 | Tnf···=·total·number·of·function·evaluations | ||
| 106 | Tnint·=·total·number·of·segments·explored·during·Cauchy·searches | ||
| 107 | Skip··=·number·of·BFGS·updates·skipped | ||
| 108 | Nact··=·number·of·active·bounds·at·final·generalized·Cauchy·point | ||
| 109 | Projg·=·norm·of·the·final·projected·gradient | ||
| 110 | F·····=·final·function·value | ||
| 111 | ···········*·*·* | ||
| 112 | ···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F | ||
| 113 | ····3······2······5······1·····0·····0···4.516D-05···1.414D+00 | ||
| 114 | ··F·=···1.4137311050015486 | ||
| 115 | CONVERGENCE:·REL_REDUCTION_OF_F_<=_FACTR*EPSMCH | ||
| 76 | The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR | 116 | The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR |
| 77 | (1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated | 117 | (1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated |
| 78 | parameters·(AR(0)·or·ARIMA),·or·depends·on·the·ratio·of·the·intercept·to·1 | 118 | parameters·(AR(0)·or·ARIMA),·or·depends·on·the·ratio·of·the·intercept·to·1 |
| 79 | minus·the·AR(1)·parameter. | 119 | minus·the·AR(1)·parameter. |
| 80 | [ | 120 | [5]: |
| 81 | intercept·=·[ | 121 | intercept·=·[ |
| 82 | ····ar0_res.params[0], | 122 | ····ar0_res.params[0], |
| 83 | ····sarimax_res.params[0], | 123 | ····sarimax_res.params[0], |
| 84 | ····arima_res.params[0], | 124 | ····arima_res.params[0], |
| 85 | ····autoreg_res.params[0], | 125 | ····autoreg_res.params[0], |
| 86 | ] | 126 | ] |
| 87 | rho_hat·=·[0]·+·[r.params[1]·for·r·in·(sarimax_res,·arima_res,·autoreg_res)] | 127 | rho_hat·=·[0]·+·[r.params[1]·for·r·in·(sarimax_res,·arima_res,·autoreg_res)] |
| Offset 18, 34 lines modified | Offset 18, 34 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":·"202 | 25 | ····················"iopub.execute_input":·"2025-05-17T08:05:32.255402Z", |
| 26 | ····················"iopub.status.busy":·"202 | 26 | ····················"iopub.status.busy":·"2025-05-17T08:05:32.254961Z", |
| 27 | ····················"iopub.status.idle":·"202 | 27 | ····················"iopub.status.idle":·"2025-05-17T08:05:33.241970Z", |
| 28 | ····················"shell.execute_reply":·"202 | 28 | ····················"shell.execute_reply":·"2025-05-17T08:05:33.233948Z" |
| 29 | ················} | 29 | ················} |
| 30 | ············}, | 30 | ············}, |
| 31 | ············"outputs":·[], | 31 | ············"outputs":·[], |
| 32 | ············"source":·[ | 32 | ············"source":·[ |
| 33 | ················"%matplotlib·inline" | 33 | ················"%matplotlib·inline" |
| 34 | ············] | 34 | ············] |
| 35 | ········}, | 35 | ········}, |
| 36 | ········{ | 36 | ········{ |
| 37 | ············"cell_type":·"code", | 37 | ············"cell_type":·"code", |
| 38 | ············"execution_count":·2, | 38 | ············"execution_count":·2, |
| 39 | ············"metadata":·{ | 39 | ············"metadata":·{ |
| 40 | ················"execution":·{ | 40 | ················"execution":·{ |
| 41 | ····················"iopub.execute_input":·"202 | 41 | ····················"iopub.execute_input":·"2025-05-17T08:05:33.254778Z", |
| 42 | ····················"iopub.status.busy":·"202 | 42 | ····················"iopub.status.busy":·"2025-05-17T08:05:33.254245Z", |
| 43 | ····················"iopub.status.idle":·"202 | 43 | ····················"iopub.status.idle":·"2025-05-17T08:05:35.105989Z", |
| 44 | ····················"shell.execute_reply":·"202 | 44 | ····················"shell.execute_reply":·"2025-05-17T08:05:35.089960Z" |
| 45 | ················} | 45 | ················} |
| 46 | ············}, | 46 | ············}, |
| 47 | ············"outputs":·[], | 47 | ············"outputs":·[], |
| 48 | ············"source":·[ | 48 | ············"source":·[ |
| 49 | ················"import·numpy·as·np\n", | 49 | ················"import·numpy·as·np\n", |
| 50 | ················"import·pandas·as·pd\n", | 50 | ················"import·pandas·as·pd\n", |
| 51 | ················"import·statsmodels.api·as·sm\n", | 51 | ················"import·statsmodels.api·as·sm\n", |
| Offset 581, 15 lines modified | Offset 581, 15 lines modified | ||
| 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_ | 588 | /tmp/ipykernel_3711/1512460390.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 194, 15 lines modified | Offset 194, 15 lines modified | ||
| 194 | p-value··················0.100000 | 194 | p-value··················0.100000 |
| 195 | Lags·Used················0.000000 | 195 | Lags·Used················0.000000 |
| 196 | Critical·Value·(10%)·····0.347000 | 196 | Critical·Value·(10%)·····0.347000 |
| 197 | Critical·Value·(5%)······0.463000 | 197 | Critical·Value·(5%)······0.463000 |
| 198 | Critical·Value·(2.5%)····0.574000 | 198 | Critical·Value·(2.5%)····0.574000 |
| 199 | Critical·Value·(1%)······0.739000 | 199 | Critical·Value·(1%)······0.739000 |
| 200 | dtype:·float64 | 200 | dtype:·float64 |
| 201 | /tmp/ipykernel_ | 201 | /tmp/ipykernel_3711/1512460390.py:6:·InterpolationWarning:·The·test·statistic |
| 202 | is·outside·of·the·range·of·p-values·available·in·the | 202 | is·outside·of·the·range·of·p-values·available·in·the |
| 203 | look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned. | 203 | look-up·table.·The·actual·p-value·is·greater·than·the·p-value·returned. |
| 204 | ··kpsstest·=·kpss(timeseries,·regression="c",·nlags="auto") | 204 | ··kpsstest·=·kpss(timeseries,·regression="c",·nlags="auto") |
| 205 | Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected. | 205 | Based·upon·the·p-value·of·KPSS·test,·the·null·hypothesis·can·not·be·rejected. |
| 206 | Hence,·the·series·is·stationary. | 206 | Hence,·the·series·is·stationary. |
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| 19 | ············] | 19 | ············] |
| 20 | ········}, | 20 | ········}, |
| 21 | ········{ | 21 | ········{ |
| 22 | ············"cell_type":·"code", | 22 | ············"cell_type":·"code", |
| 23 | ············"execution_count":·1, | 23 | ············"execution_count":·1, |
| 24 | ············"metadata":·{ | 24 | ············"metadata":·{ |
| 25 | ················"execution":·{ | 25 | ················"execution":·{ |
| 26 | ····················"iopub.execute_input":·"202 | 26 | ····················"iopub.execute_input":·"2025-05-17T08:05:10.886380Z", |
| 27 | ····················"iopub.status.busy":·"202 | 27 | ····················"iopub.status.busy":·"2025-05-17T08:05:10.886100Z", |
| 28 | ····················"iopub.status.idle":·"202 | 28 | ····················"iopub.status.idle":·"2025-05-17T08:05:13.220180Z", |
| 29 | ····················"shell.execute_reply":·"202 | 29 | ····················"shell.execute_reply":·"2025-05-17T08:05:13.214937Z" |
| 30 | ················} | 30 | ················} |
| 31 | ············}, | 31 | ············}, |
| 32 | ············"outputs":·[], | 32 | ············"outputs":·[], |
| 33 | ············"source":·[ | 33 | ············"source":·[ |
| 34 | ················"%matplotlib·inline\n", | 34 | ················"%matplotlib·inline\n", |
| 35 | ················"import·matplotlib.pyplot·as·plt\n", | 35 | ················"import·matplotlib.pyplot·as·plt\n", |
| 36 | ················"import·numpy·as·np\n", | 36 | ················"import·numpy·as·np\n", |
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| 21 | ········}, | 21 | ········}, |
| 22 | ········{ | 22 | ········{ |
| 23 | ············"cell_type":·"code", | 23 | ············"cell_type":·"code", |
| 24 | ············"execution_count":·1, | 24 | ············"execution_count":·1, |
| 25 | ············"id":·"59f2450e", | 25 | ············"id":·"59f2450e", |
| 26 | ············"metadata":·{ | 26 | ············"metadata":·{ |
| 27 | ················"execution":·{ | 27 | ················"execution":·{ |
| 28 | ····················"iopub.execute_input":·"202 | 28 | ····················"iopub.execute_input":·"2025-05-17T08:05:10.876263Z", |
| 29 | ····················"iopub.status.busy":·"202 | 29 | ····················"iopub.status.busy":·"2025-05-17T08:05:10.875881Z", |
| 30 | ····················"iopub.status.idle":·"202 | 30 | ····················"iopub.status.idle":·"2025-05-17T08:05:11.746896Z", |
| 31 | ····················"shell.execute_reply":·"202 | 31 | ····················"shell.execute_reply":·"2025-05-17T08:05:11.745942Z" |
| 32 | ················} | 32 | ················} |
| 33 | ············}, | 33 | ············}, |
| 34 | ············"outputs":·[], | 34 | ············"outputs":·[], |
| 35 | ············"source":·[ | 35 | ············"source":·[ |
| 36 | ················"import·numpy·as·np\n", | 36 | ················"import·numpy·as·np\n", |
| 37 | ················"from·numpy.testing·import·assert_allclose\n", | 37 | ················"from·numpy.testing·import·assert_allclose\n", |
| 38 | ················"import·statsmodels.stats.rates·as·smr\n", | 38 | ················"import·statsmodels.stats.rates·as·smr\n", |
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| 23 | ········}, | 23 | ········}, |
| 24 | ········{ | 24 | ········{ |
| 25 | ············"cell_type":·"code", | 25 | ············"cell_type":·"code", |
| 26 | ············"execution_count":·1, | 26 | ············"execution_count":·1, |
| 27 | ············"id":·"2b591408", | 27 | ············"id":·"2b591408", |
| 28 | ············"metadata":·{ | 28 | ············"metadata":·{ |
| 29 | ················"execution":·{ | 29 | ················"execution":·{ |
| 30 | ····················"iopub.execute_input":·"202 | 30 | ····················"iopub.execute_input":·"2025-05-17T08:05:21.703720Z", |
| 31 | ····················"iopub.status.busy":·"202 | 31 | ····················"iopub.status.busy":·"2025-05-17T08:05:21.703277Z", |
| 32 | ····················"iopub.status.idle":·"202 | 32 | ····················"iopub.status.idle":·"2025-05-17T08:05:22.917993Z", |
| 33 | ····················"shell.execute_reply":·"202 | 33 | ····················"shell.execute_reply":·"2025-05-17T08:05:22.906976Z" |
| 34 | ················} | 34 | ················} |
| 35 | ············}, | 35 | ············}, |
| 36 | ············"outputs":·[], | 36 | ············"outputs":·[], |
| 37 | ············"source":·[ | 37 | ············"source":·[ |
| 38 | ················"import·numpy·as·np\n", | 38 | ················"import·numpy·as·np\n", |
| 39 | ················"\n", | 39 | ················"\n", |
| 40 | ················"from·statsmodels.stats.nonparametric·import·(\n", | 40 | ················"from·statsmodels.stats.nonparametric·import·(\n", |
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| 889 | </div> | 889 | </div> |
| 890 | </div> | 890 | </div> |
| 891 | <div·class="nboutput·docutils·container"> | 891 | <div·class="nboutput·docutils·container"> |
| 892 | <div·class="prompt·empty·docutils·container"> | 892 | <div·class="prompt·empty·docutils·container"> |
| 893 | </div> | 893 | </div> |
| 894 | <div·class="output_area·docutils·container"> | 894 | <div·class="output_area·docutils·container"> |
| 895 | <div·class="highlight"><pre> | 895 | <div·class="highlight"><pre> |
| 896 | 896 | 226·ms·±·1.64·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"·/> |
| Offset 516, 15 lines modified | Offset 516, 15 lines modified | ||
| 516 | [../../../_images/examples_notebooks_generated_stl_decomposition_15_0.png] | 516 | [../../../_images/examples_notebooks_generated_stl_decomposition_15_0.png] |
| 517 | First,·the·base·line·model·is·estimated·with·all·jumps·equal·to·1. | 517 | First,·the·base·line·model·is·estimated·with·all·jumps·equal·to·1. |
| 518 | [10]: | 518 | [10]: |
| 519 | mod·=·STL(y,·period=period,·seasonal=seasonal) | 519 | mod·=·STL(y,·period=period,·seasonal=seasonal) |
| 520 | %timeit·mod.fit() | 520 | %timeit·mod.fit() |
| 521 | res·=·mod.fit() | 521 | res·=·mod.fit() |
| 522 | fig·=·res.plot(observed=False,·resid=False) | 522 | fig·=·res.plot(observed=False,·resid=False) |
| 523 | 523 | 226·ms·Â±·1.64·ms·per·loop·(mean·Â±·std.·dev.·of·7·runs,·1·loop·each) | |
| 524 | [../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png] | 524 | [../../../_images/examples_notebooks_generated_stl_decomposition_17_1.png] |
| 525 | The·jumps·are·all·set·to·15%·of·their·window·length.·Limited·linear | 525 | The·jumps·are·all·set·to·15%·of·their·window·length.·Limited·linear |
| 526 | interpolation·makes·little·difference·to·the·fit·of·the·model. | 526 | interpolation·makes·little·difference·to·the·fit·of·the·model. |
| 527 | [11]: | 527 | [11]: |
| 528 | low_pass_jump·=·seasonal_jump·=·int(0.15·*·(period·+·1)) | 528 | low_pass_jump·=·seasonal_jump·=·int(0.15·*·(period·+·1)) |
| 529 | trend_jump·=·int(0.15·*·1.5·*·(period·+·1)) | 529 | trend_jump·=·int(0.15·*·1.5·*·(period·+·1)) |
| 530 | mod·=·STL( | 530 | mod·=·STL( |
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| 16 | ············] | 16 | ············] |
| 17 | ········}, | 17 | ········}, |
| 18 | ········{ | 18 | ········{ |
| 19 | ············"cell_type":·"code", | 19 | ············"cell_type":·"code", |
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| 21 | ············"metadata":·{ | 21 | ············"metadata":·{ |
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| 23 | ····················"iopub.execute_input":·"202 | 23 | ····················"iopub.execute_input":·"2025-05-17T08:05:28.948557Z", |
| 24 | ····················"iopub.status.busy":·"202 | 24 | ····················"iopub.status.busy":·"2025-05-17T08:05:28.948128Z", |
| 25 | ····················"iopub.status.idle":·"202 | 25 | ····················"iopub.status.idle":·"2025-05-17T08:05:30.721972Z", |
| 26 | ····················"shell.execute_reply":·"202 | 26 | ····················"shell.execute_reply":·"2025-05-17T08:05:30.701993Z" |
| 27 | ················} | 27 | ················} |
| 28 | ············}, | 28 | ············}, |
| 29 | ············"outputs":·[], | 29 | ············"outputs":·[], |
| 30 | ············"source":·[ | 30 | ············"source":·[ |
| 31 | ················"import·matplotlib.pyplot·as·plt\n", | 31 | ················"import·matplotlib.pyplot·as·plt\n", |
| 32 | ················"import·pandas·as·pd\n", | 32 | ················"import·pandas·as·pd\n", |
| 33 | ················"import·seaborn·as·sns\n", | 33 | ················"import·seaborn·as·sns\n", |
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| 26 | ········}, | 26 | ········}, |
| 27 | ········{ | 27 | ········{ |
| 28 | ············"cell_type":·"code", | 28 | ············"cell_type":·"code", |
| 29 | ············"execution_count":·1, | 29 | ············"execution_count":·1, |
| 30 | ············"id":·"adult-capture", | 30 | ············"id":·"adult-capture", |
| 31 | ············"metadata":·{ | 31 | ············"metadata":·{ |
| 32 | ················"execution":·{ | 32 | ················"execution":·{ |
| 33 | ····················"iopub.execute_input":·"202 | 33 | ····················"iopub.execute_input":·"2025-05-17T08:05:19.511363Z", |
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| 35 | ····················"iopub.status.idle":·"202 | 35 | ····················"iopub.status.idle":·"2025-05-17T08:05:21.181976Z", |
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| 37 | ················} | 37 | ················} |
| 38 | ············}, | 38 | ············}, |
| 39 | ············"outputs":·[], | 39 | ············"outputs":·[], |
| 40 | ············"source":·[ | 40 | ············"source":·[ |
| 41 | ················"import·os\n", | 41 | ················"import·os\n", |
| 42 | ················"import·numpy·as·np\n", | 42 | ················"import·numpy·as·np\n", |
| 43 | ················"from·numpy.testing·import·assert_allclose\n", | 43 | ················"from·numpy.testing·import·assert_allclose\n", |
| Offset 906, 25 lines modified | Offset 906, 14 lines modified | ||
| 906 | <span·class="nb">print</span><span·class="p">(</span><span·class="n">table</span><span·class="o">.</span><span·class="n">set_index</span><span·class="p">(</span><span·class="s2">"lag"</span><span·class="p">))</span> | 906 | <span·class="nb">print</span><span·class="p">(</span><span·class="n">table</span><span·class="o">.</span><span·class="n">set_index</span><span·class="p">(</span><span·class="s2">"lag"</span><span·class="p">))</span> |
| 907 | </pre></div> | 907 | </pre></div> |
| 908 | </div> | 908 | </div> |
| 909 | </div> | 909 | </div> |
| 910 | <div·class="nboutput·docutils·container"> | 910 | <div·class="nboutput·docutils·container"> |
| 911 | <div·class="prompt·empty·docutils·container"> | 911 | <div·class="prompt·empty·docutils·container"> |
| 912 | </div> | 912 | </div> |
| 913 | <div·class="output_area·stderr·docutils·container"> | ||
| 914 | <div·class="highlight"><pre> | ||
| 915 | /usr/lib/python3/dist-packages/statsmodels/tsa/statespace/sarimax.py:966:·UserWarning:·Non-stationary·starting·autoregressive·parameters·found.·Using·zeros·as·starting·parameters. | ||
| 916 | ··warn('Non-stationary·starting·autoregressive·parameters' | ||
| 917 | /usr/lib/python3/dist-packages/statsmodels/tsa/statespace/sarimax.py:978:·UserWarning:·Non-invertible·starting·MA·parameters·found.·Using·zeros·as·starting·parameters. | ||
| 918 | ··warn('Non-invertible·starting·MA·parameters·found.' | ||
| 919 | </pre></div></div> | ||
| 920 | </div> | ||
| 921 | <div·class="nboutput·nblast·docutils·container"> | ||
| 922 | <div·class="prompt·empty·docutils·container"> | ||
| 923 | </div> | ||
| 924 | <div·class="output_area·docutils·container"> | 913 | <div·class="output_area·docutils·container"> |
| 925 | <div·class="highlight"><pre> | 914 | <div·class="highlight"><pre> |
| 926 | ············AC···········Q······Prob(>Q) | 915 | ············AC···········Q······Prob(>Q) |
| 927 | lag | 916 | lag |
| 928 | 1.0··-0.001244····0.000778··9.777436e-01 | 917 | 1.0··-0.001244····0.000778··9.777436e-01 |
| 929 | 2.0···0.052350····1.382049··5.010626e-01 | 918 | 2.0···0.052350····1.382049··5.010626e-01 |
| 930 | 3.0··-0.522181··139.090106··5.938063e-30 | 919 | 3.0··-0.522181··139.090106··5.938063e-30 |
| Offset 243, 22 lines modified | Offset 243, 14 lines modified | ||
| 243 | lags·=·int(10·*·np.log10(arma_rvs.shape[0])) | 243 | lags·=·int(10·*·np.log10(arma_rvs.shape[0])) |
| 244 | arma11·=·ARIMA(arma_rvs,·order=(1,·0,·1)).fit() | 244 | arma11·=·ARIMA(arma_rvs,·order=(1,·0,·1)).fit() |
| 245 | resid·=·arma11.resid | 245 | resid·=·arma11.resid |
| 246 | r,·q,·p·=·sm.tsa.acf(resid,·nlags=lags,·fft=True,·qstat=True) | 246 | r,·q,·p·=·sm.tsa.acf(resid,·nlags=lags,·fft=True,·qstat=True) |
| 247 | data·=·np.c_[range(1,·lags·+·1),·r[1:],·q,·p] | 247 | data·=·np.c_[range(1,·lags·+·1),·r[1:],·q,·p] |
| 248 | table·=·pd.DataFrame(data,·columns=["lag",·"AC",·"Q",·"Prob(>Q)"]) | 248 | table·=·pd.DataFrame(data,·columns=["lag",·"AC",·"Q",·"Prob(>Q)"]) |
| 249 | print(table.set_index("lag")) | 249 | print(table.set_index("lag")) |
| 250 | /usr/lib/python3/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: | ||
| 251 | UserWarning:·Non-stationary·starting·autoregressive·parameters·found.·Using | ||
| 252 | zeros·as·starting·parameters. | ||
| 253 | ··warn('Non-stationary·starting·autoregressive·parameters' | ||
| 254 | /usr/lib/python3/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: | ||
| 255 | UserWarning:·Non-invertible·starting·MA·parameters·found.·Using·zeros·as | ||
| 256 | starting·parameters. | ||
| 257 | ··warn('Non-invertible·starting·MA·parameters·found.' | ||
| 258 | ············AC···········Q······Prob(>Q) | 250 | ············AC···········Q······Prob(>Q) |
| 259 | lag | 251 | lag |
| 260 | 1.0··-0.001244····0.000778··9.777436e-01 | 252 | 1.0··-0.001244····0.000778··9.777436e-01 |
| 261 | 2.0···0.052350····1.382049··5.010626e-01 | 253 | 2.0···0.052350····1.382049··5.010626e-01 |
| 262 | 3.0··-0.522181··139.090106··5.938063e-30 | 254 | 3.0··-0.522181··139.090106··5.938063e-30 |
| 263 | 4.0···0.146506··149.951983··2.084573e-31 | 255 | 4.0···0.146506··149.951983··2.084573e-31 |
| 264 | 5.0··-0.091171··154.166872··1.731083e-31 | 256 | 5.0··-0.091171··154.166872··1.731083e-31 |
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| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"%matplotlib·inline" | 23 | ················"%matplotlib·inline" |
| 24 | ············] | 24 | ············] |
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| 29 | ············"metadata":·{ | 29 | ············"metadata":·{ |
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| 35 | ················} | 35 | ················} |
| 36 | ············}, | 36 | ············}, |
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| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"import·matplotlib.pyplot·as·plt\n", | 39 | ················"import·matplotlib.pyplot·as·plt\n", |
| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
| 41 | ················"import·pandas·as·pd\n", | 41 | ················"import·pandas·as·pd\n", |
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| 35 | ················} | 35 | ················} |
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| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"import·numpy·as·np\n", | 39 | ················"import·numpy·as·np\n", |
| 40 | ················"import·pandas·as·pd\n", | 40 | ················"import·pandas·as·pd\n", |
| 41 | ················"\n", | 41 | ················"\n", |
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| 39 | ················"import·pandas·as·pd\n", | 39 | ················"import·pandas·as·pd\n", |
| 40 | ················"import·matplotlib.pyplot·as·plt\n", | 40 | ················"import·matplotlib.pyplot·as·plt\n", |
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| 26 | ················"import·numpy·as·np\n", | 26 | ················"import·numpy·as·np\n", |
| 27 | ················"import·statsmodels.api·as·sm\n", | 27 | ················"import·statsmodels.api·as·sm\n", |
| 28 | ················"from·statsmodels.regression.mixed_linear_model·import·VCSpec\n", | 28 | ················"from·statsmodels.regression.mixed_linear_model·import·VCSpec\n", |
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| 17 | ····················"iopub.status.idle":·"202 | 17 | ····················"iopub.status.idle":·"2025-05-17T08:05:12.439021Z", |
| 18 | ····················"shell.execute_reply":·"202 | 18 | ····················"shell.execute_reply":·"2025-05-17T08:05:12.438136Z" |
| 19 | ················} | 19 | ················} |
| 20 | ············}, | 20 | ············}, |
| 21 | ············"outputs":·[], | 21 | ············"outputs":·[], |
| 22 | ············"source":·[ | 22 | ············"source":·[ |
| 23 | ················"%matplotlib·inline" | 23 | ················"%matplotlib·inline" |
| 24 | ············] | 24 | ············] |
| 25 | ········}, | 25 | ········}, |
| 26 | ········{ | 26 | ········{ |
| 27 | ············"cell_type":·"code", | 27 | ············"cell_type":·"code", |
| 28 | ············"execution_count":·2, | 28 | ············"execution_count":·2, |
| 29 | ············"metadata":·{ | 29 | ············"metadata":·{ |
| 30 | ················"execution":·{ | 30 | ················"execution":·{ |
| 31 | ····················"iopub.execute_input":·"202 | 31 | ····················"iopub.execute_input":·"2025-05-17T08:05:12.445980Z", |
| 32 | ····················"iopub.status.busy":·"202 | 32 | ····················"iopub.status.busy":·"2025-05-17T08:05:12.445489Z", |
| 33 | ····················"iopub.status.idle":·"202 | 33 | ····················"iopub.status.idle":·"2025-05-17T08:05:13.743590Z", |
| 34 | ····················"shell.execute_reply":·"202 | 34 | ····················"shell.execute_reply":·"2025-05-17T08:05:13.742636Z" |
| 35 | ················} | 35 | ················} |
| 36 | ············}, | 36 | ············}, |
| 37 | ············"outputs":·[], | 37 | ············"outputs":·[], |
| 38 | ············"source":·[ | 38 | ············"source":·[ |
| 39 | ················"import·matplotlib.pyplot·as·plt\n", | 39 | ················"import·matplotlib.pyplot·as·plt\n", |
| 40 | ················"import·numpy·as·np\n", | 40 | ················"import·numpy·as·np\n", |
| 41 | ················"import·statsmodels.api·as·sm\n", | 41 | ················"import·statsmodels.api·as·sm\n", |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | ········"taylor":·[0,·212,·267,·3957,·3959,·6432], | 15 | ········"taylor":·[0,·212,·267,·3957,·3959,·6432], |
| 16 | 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| 18 | 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| 18 | 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| 20 | ········"later":·[0,·214,·221,·224,·237,·3957,·4791,·6087], | 20 | ········"later":·[0,·214,·221,·224,·237,·3957,·4791,·6087], |
| 21 | ········"remov":·[0,·66,·81,·104,·113,·173,·212,·223,·224,·234,·235,·237,·245,·247,·252,·254,·257,·275,·284,·347,·356,·404,·425,·462,·483,·520,·541,·577,·598,·632,·653,·687,·707,·737,·745,·768,·810,·831,·888,·910,·939,·959,·967,·990,·1023,·1053,·1074,·1109,·1130,·1183,·1204,·1223,·1244,·1430,·1441,·1521,·1535,·1569,·1613,·1940,·1970,·1991,·2038,·2067,·2091,·2102,·2111,·2129,·2168,·2178,·2211,·2219,·2220,·2278,·2291,·2351,·2382,·2402,·2544,·2573,·2598,·2618,·2728,·2792,·2829,·2856,·2874,·2908,·2925,·2990,·3061,·3103,·3132,·3151,·3225,·3235,·3501,·3514,·3562,·3576,·3625,·3739,·3916,·3921,·3947,·3957,·3958,·4179,·4276,·4282,·4303,·4324,·4340,·4341,·4350,·4382,·4403,·4427,·4436,·4468,·4489,·4571,·4604,·4651,·4765,·4783,·4800,·4806,·4807,·4809,·4818,·4837,·4850,·4860,·4869,·4885,·4960,·5019,·5051,·5126,·5159,·5229,·5259,·5539,·5569,·5702,·5735,·5920,·5950,·5955,·6035,·6065,·6082,·6083,·6412,·6421,·6431,·6432,·6434,·6435,·6439,·6441,·6444,·6445,·6446,·6447,·6450,·6458], | 21 | ········"remov":·[0,·66,·81,·104,·113,·173,·212,·223,·224,·234,·235,·237,·245,·247,·252,·254,·257,·275,·284,·347,·356,·404,·425,·462,·483,·520,·541,·577,·598,·632,·653,·687,·707,·737,·745,·768,·810,·831,·888,·910,·939,·959,·967,·990,·1023,·1053,·1074,·1109,·1130,·1183,·1204,·1223,·1244,·1430,·1441,·1521,·1535,·1569,·1613,·1940,·1970,·1991,·2038,·2067,·2091,·2102,·2111,·2129,·2168,·2178,·2211,·2219,·2220,·2278,·2291,·2351,·2382,·2402,·2544,·2573,·2598,·2618,·2728,·2792,·2829,·2856,·2874,·2908,·2925,·2990,·3061,·3103,·3132,·3151,·3225,·3235,·3501,·3514,·3562,·3576,·3625,·3739,·3916,·3921,·3947,·3957,·3958,·4179,·4276,·4282,·4303,·4324,·4340,·4341,·4350,·4382,·4403,·4427,·4436,·4468,·4489,·4571,·4604,·4651,·4765,·4783,·4800,·4806,·4807,·4809,·4818,·4837,·4850,·4860,·4869,·4885,·4960,·5019,·5051,·5126,·5159,·5229,·5259,·5539,·5569,·5702,·5735,·5920,·5950,·5955,·6035,·6065,·6082,·6083,·6412,·6421,·6431,·6432,·6434,·6435,·6439,·6441,·6444,·6445,·6446,·6447,·6450,·6458], |
| 22 | ········"dure":·[0,·5,·102,·153,·185,·201,·216,·217,·221,·224,·243,·245,·257,·258,·2080,·2237,·2833,·3088,·3481,·3539,·3648,·3670,·3920,·4593,·5042,·5118,·5150,·5222,·5251,·5276,·5282,·5291,·5311,·5388,·5408,·5473,·5561,·5626,·5724,·5776,·5797,·5945,·6057,·6409,·6410,·6421,·6428,·6435,·6446,·6449,·6450], | 22 | ········"dure":·[0,·5,·102,·153,·185,·201,·216,·217,·221,·224,·243,·245,·246,·257,·258,·2080,·2237,·2833,·3088,·3481,·3539,·3648,·3670,·3920,·4593,·5042,·5118,·5150,·5222,·5251,·5276,·5282,·5291,·5311,·5388,·5408,·5473,·5561,·5626,·5724,·5776,·5797,·5945,·6057,·6409,·6410,·6421,·6428,·6435,·6446,·6449,·6450], |
| 23 | ········"googl":·[0,·6431,·6450], | 23 | ········"googl":·[0,·6431,·6450], |
| 24 | ········"summer":·[0,·221,·6431,·6450], | 24 | ········"summer":·[0,·221,·6431,·6450], |
| 25 | ········"2009":·[0,·23,·34,·202,·224,·236,·238,·243,·245,·252,·260,·262,·263,·2194,·3764,·3899,·3957,·3958,·3959,·4017,·4135,·4250,·4251,·4252,·4625,·4644,·4961,·5068,·6423,·6425,·6446,·6447,·6448], | 25 | ········"2009":·[0,·23,·34,·202,·224,·236,·238,·243,·245,·252,·260,·262,·263,·2194,·3764,·3899,·3957,·3958,·3959,·4017,·4135,·4250,·4251,·4252,·4625,·4644,·4961,·5068,·6423,·6425,·6446,·6447,·6448], |
| 26 | ········"correct":·[0,·62,·86,·117,·131,·182,·187,·198,·209,·223,·226,·231,·233,·234,·241,·250,·265,·288,·360,·414,·430,·435,·472,·488,·493,·530,·546,·551,·586,·594,·603,·608,·642,·658,·663,·696,·711,·716,·755,·773,·778,·819,·827,·837,·842,·897,·906,·915,·920,·977,·995,·1000,·1062,·1070,·1080,·1085,·1119,·1135,·1140,·1193,·1209,·1214,·1233,·1249,·1254,·1356,·1448,·1503,·1550,·1578,·1582,·1830,·1860,·1861,·1867,·1885,·1891,·1919,·1971,·2012,·2017,·2046,·2075,·2112,·2138,·2142,·2182,·2210,·2224,·2378,·2408,·2524,·2527,·2534,·2537,·2569,·2606,·2621,·2634,·2695,·2697,·2715,·2716,·2725,·2739,·2763,·2765,·2780,·2781,·2803,·2810,·2850,·2880,·2904,·2930,·2959,·2961,·2976,·2977,·3001,·3055,·3114,·3242,·3259,·3284,·3309,·3334,·3365,·3390,·3421,·3446,·3481,·3518,·3526,·3539,·3582,·3596,·3598,·3613,·3614,·3637,·3648,·3670,·3710,·3712,·3741,·3742,·3743,·3744,·3746,·3748,·3750,·3751,·3753,·3779,·3798,·3800,·3828,·3875,·3881,·3882,·3885,·3902,·3907,·3916,·3917,·3920,·3927,·3930,·3931,·3934,·3957,·3958,·3959,·3977,·3978,·3980,·3981,·3982,·4000,·4010,·4011,·4015,·4016,·4017,·4018,·4024,·4026,·4043,·4088,·4090,·4091,·4113,·4118,·4125,·4126,·4127,·4132,·4133,·4134,·4135,·4145,·4165,·4166,·4167,·4172,·4173,·4174,·4195,·4204,·4205,·4213,·4214,·4216,·4224,·4231,·4232,·4282,·4294,·4296,·4332,·4341,·4350,·4373,·4375,·4411,·4436,·4450,·4452,·4458,·4497,·4563,·4614,·4760,·4762,·4790,·4860,·4862,·4956,·5013,·5059,·5118,·5120,·5167,·5222,·5224,·5267,·5534,·5577,·5694,·5745,·5914,·5964,·5975,·6030,·6073,·6097,·6184,·6284,·6354,·6365,·6409,·6410,·6416,·6426,·6428,·6431,·6432,·6435,·6436,·6437,·6438,·6439,·6441,·6444,·6445,·6446,·6447,·6455], | 26 | ········"correct":·[0,·62,·86,·117,·131,·182,·187,·198,·209,·223,·226,·231,·233,·234,·241,·250,·265,·288,·360,·414,·430,·435,·472,·488,·493,·530,·546,·551,·586,·594,·603,·608,·642,·658,·663,·696,·711,·716,·755,·773,·778,·819,·827,·837,·842,·897,·906,·915,·920,·977,·995,·1000,·1062,·1070,·1080,·1085,·1119,·1135,·1140,·1193,·1209,·1214,·1233,·1249,·1254,·1356,·1448,·1503,·1550,·1578,·1582,·1830,·1860,·1861,·1867,·1885,·1891,·1919,·1971,·2012,·2017,·2046,·2075,·2112,·2138,·2142,·2182,·2210,·2224,·2378,·2408,·2524,·2527,·2534,·2537,·2569,·2606,·2621,·2634,·2695,·2697,·2715,·2716,·2725,·2739,·2763,·2765,·2780,·2781,·2803,·2810,·2850,·2880,·2904,·2930,·2959,·2961,·2976,·2977,·3001,·3055,·3114,·3242,·3259,·3284,·3309,·3334,·3365,·3390,·3421,·3446,·3481,·3518,·3526,·3539,·3582,·3596,·3598,·3613,·3614,·3637,·3648,·3670,·3710,·3712,·3741,·3742,·3743,·3744,·3746,·3748,·3750,·3751,·3753,·3779,·3798,·3800,·3828,·3875,·3881,·3882,·3885,·3902,·3907,·3916,·3917,·3920,·3927,·3930,·3931,·3934,·3957,·3958,·3959,·3977,·3978,·3980,·3981,·3982,·4000,·4010,·4011,·4015,·4016,·4017,·4018,·4024,·4026,·4043,·4088,·4090,·4091,·4113,·4118,·4125,·4126,·4127,·4132,·4133,·4134,·4135,·4145,·4165,·4166,·4167,·4172,·4173,·4174,·4195,·4204,·4205,·4213,·4214,·4216,·4224,·4231,·4232,·4282,·4294,·4296,·4332,·4341,·4350,·4373,·4375,·4411,·4436,·4450,·4452,·4458,·4497,·4563,·4614,·4760,·4762,·4790,·4860,·4862,·4956,·5013,·5059,·5118,·5120,·5167,·5222,·5224,·5267,·5534,·5577,·5694,·5745,·5914,·5964,·5975,·6030,·6073,·6097,·6184,·6284,·6354,·6365,·6409,·6410,·6416,·6426,·6428,·6431,·6432,·6435,·6436,·6437,·6438,·6439,·6441,·6444,·6445,·6446,·6447,·6455], |
| 27 | ········"improv":·[0,·4,·28,·197,·206,·217,·237,·238,·245,·252,·268,·1356,·2156,·2696,·2764,·2960,·3125,·3160,·3597,·3911,·3912,·3913,·3914,·3957,·3999,·4011,·4282,·4350,·4436,·4458,·4900,·4925,·5346,·5445,·5614,·5834,·5974,·6431,·6432,·6433,·6434,·6436,·6437,·6438,·6439,·6440,·6441,·6442,·6444,·6445,·6447,·6448,·6454], | 27 | ········"improv":·[0,·4,·28,·197,·206,·217,·237,·238,·245,·252,·268,·1356,·2156,·2696,·2764,·2960,·3125,·3160,·3597,·3911,·3912,·3913,·3914,·3957,·3999,·4011,·4282,·4350,·4436,·4458,·4900,·4925,·5346,·5445,·5614,·5834,·5974,·6431,·6432,·6433,·6434,·6436,·6437,·6438,·6439,·6440,·6441,·6442,·6444,·6445,·6447,·6448,·6454], |
| 28 | ········"releas":·[0,·3,·66,·89,·90,·104,·120,·121,·175,·179,·195,·245,·275,·291,·292,·347,·363,·364,·404,·438,·439,·462,·496,·497,·520,·554,·555,·577,·611,·612,·632,·666,·667,·687,·719,·720,·745,·781,·782,·810,·845,·846,·888,·923,·924,·967,·1003,·1004,·1053,·1088,·1089,·1109,·1143,·1144,·1183,·1217,·1218,·1223,·1257,·1258,·1430,·1451,·1452,·1535,·1586,·1587,·1970,·2015,·2016,·2102,·2111,·2145,·2146,·2168,·2185,·2186,·2382,·2411,·2412,·2573,·2609,·2610,·2743,·2744,·2807,·2808,·2856,·2883,·2884,·2908,·2933,·2934,·3005,·3006,·3061,·3121,·3122,·3132,·3225,·3245,·3246,·3501,·3521,·3522,·3562,·3585,·3586,·3641,·3642,·4263,·4276,·4303,·4338,·4339,·4340,·4382,·4417,·4418,·4468,·4503,·4504,·4571,·4620,·4621,·4765,·4796,·4797,·5019,·5065,·5066,·5068,·5126,·5173,·5174,·5229,·5273,·5274,·5476,·5539,·5583,·5584,·5598,·5599,·5604,·5605,·5702,·5751,·5752,·5920,·5971,·5972,·6035,·6079,·6080,·6416,·6417], | 28 | ········"releas":·[0,·3,·66,·89,·90,·104,·120,·121,·175,·179,·195,·245,·275,·291,·292,·347,·363,·364,·404,·438,·439,·462,·496,·497,·520,·554,·555,·577,·611,·612,·632,·666,·667,·687,·719,·720,·745,·781,·782,·810,·845,·846,·888,·923,·924,·967,·1003,·1004,·1053,·1088,·1089,·1109,·1143,·1144,·1183,·1217,·1218,·1223,·1257,·1258,·1430,·1451,·1452,·1535,·1586,·1587,·1970,·2015,·2016,·2102,·2111,·2145,·2146,·2168,·2185,·2186,·2382,·2411,·2412,·2573,·2609,·2610,·2743,·2744,·2807,·2808,·2856,·2883,·2884,·2908,·2933,·2934,·3005,·3006,·3061,·3121,·3122,·3132,·3225,·3245,·3246,·3501,·3521,·3522,·3562,·3585,·3586,·3641,·3642,·4263,·4276,·4303,·4338,·4339,·4340,·4382,·4417,·4418,·4468,·4503,·4504,·4571,·4620,·4621,·4765,·4796,·4797,·5019,·5065,·5066,·5068,·5126,·5173,·5174,·5229,·5273,·5274,·5476,·5539,·5583,·5584,·5598,·5599,·5604,·5605,·5702,·5751,·5752,·5920,·5971,·5972,·6035,·6079,·6080,·6416,·6417], |
| 29 | ········"new":·[0,·6,·24,·26,·29,·39,·40,·73,·81,·113,·174,·175,·177,·183,·184,·188,·189,·191,·195,·203,·209,·226,·233,·238,·239,·241,·242,·243,·244,·248,·249,·250,·252,·254,·255,·256,·259,·263,·284,·356,·412,·414,·425,·470,·472,·483,·528,·530,·541,·562,·584,·586,·598,·640,·642,·653,·694,·696,·707,·753,·755,·768,·790,·817,·819,·831,·853,·873,·897,·910,·975,·977,·990,·1012,·1033,·1060,·1062,·1074,·1090,·1117,·1119,·1130,·1145,·1162,·1191,·1193,·1204,·1231,·1233,·1244,·1264,·1265,·1266,·1273,·1274,·1275,·1283,·1290,·1291,·1292,·1300,·1301,·1303,·1314,·1315,·1316,·1324,·1325,·1326,·1335,·1336,·1337,·1347,·1348,·1349,·1353,·1369,·1370,·1441,·1509,·1547,·1550,·1563,·1569,·1595,·1614,·1616,·1928,·1970,·1971,·1984,·1985,·1991,·2026,·2055,·2075,·2081,·2111,·2112,·2124,·2129,·2147,·2178,·2188,·2189,·2191,·2192,·2193,·2195,·2196,·2197,·2199,·2200,·2201,·2208,·2209,·2210,·2211,·2212,·2214,·2215,·2216,·2217,·2219,·2220,·2221,·2222,·2223,·2224,·2225,·2375,·2389,·2402,·2403,·2446,·2481,·2482,·2545,·2585,·2598,·2714,·2715,·2716,·2728,·2779,·2780,·2781,·2792,·2874,·2885,·2917,·2925,·2935,·2975,·2976,·2977,·2990,·3009,·3019,·3028,·3030,·3043,·3052,·3056,·3057,·3072,·3080,·3081,·3096,·3097,·3098,·3099,·3103,·3108,·3149,·3151,·3192,·3235,·3239,·3274,·3275,·3299,·3300,·3324,·3325,·3349,·3350,·3380,·3381,·3405,·3406,·3436,·3437,·3461,·3462,·3514,·3576,·3612,·3613,·3614,·3625,·3734,·3739,·3761,·3764,·3778,·3784,·3881,·3898,·3904,·3906,·3908,·3950,·3978,·4037,·4052,·4072,·4135,·4137,·4138,·4146,·4147,·4157,·4255,·4264,·4276,·4297,·4298,·4320,·4321,·4324,·4340,·4376,·4377,·4399,·4400,·4403,·4453,·4454,·4485,·4486,·4489,·4507,·4517,·4531,·4533,·4551,·4560,·4564,·4565,·4579,·4587,·4588,·4601,·4604,·4609,·4625,·4634,·4644,·4753,·4783,·4830,·4896,·4921,·4954,·4966,·4967,·4977,·4986,·4988,·5001,·5010,·5014,·5015,·5027,·5036,·5037,·5047,·5048,·5051,·5054,·5068,·5069,·5081,·5091,·5094,·5107,·5117,·5121,·5122,·5134,·5144,·5145,·5155,·5156,·5159,·5162,·5176,·5177,·5187,·5197,·5199,·5212,·5221,·5225,·5226,·5237,·5245,·5246,·5256,·5259,·5262,·5278,·5284,·5290,·5306,·5346,·5367,·5381,·5387,·5403,·5445,·5477,·5488,·5498,·5507,·5509,·5522,·5531,·5535,·5536,·5547,·5555,·5556,·5566,·5569,·5572,·5616,·5621,·5637,·5638,·5648,·5662,·5664,·5682,·5691,·5695,·5696,·5710,·5718,·5719,·5732,·5735,·5740,·5754,·5759,·5769,·5775,·5792,·5834,·5836,·5866,·5876,·5886,·5888,·5902,·5911,·5915,·5916,·5929,·5938,·5939,·5950,·5951,·5955,·5959,·5983,·5984,·5994,·6003,·6005,·6018,·6027,·6031,·6032,·6043,·6051,·6052,·6062,·6065,·6068,·6105,·6231,·6232,·6234,·6245,·6329,·6330,·6332,·6339,·6354,·6357,·6365,·6390,·6396,·6397,·6399,·6406,·6420,·6431,·6433,·6434,·6436,·6438,·6442,·6451,·6453,·6454,·6460], | 29 | 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