http://digida.mgpu.ru/index.php?action=history&feed=atom&title=%D0%90%D0%B2%D1%82%D0%BE%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F_%D1%83%D1%80%D0%BE%D0%B2%D0%BD%D0%B5%D0%B9_%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D1%8F%D0%B4%D0%B0 2026-04-16T21:51:24Z История изменений этой страницы в вики MediaWiki 1.44.0 http://digida.mgpu.ru/index.php?title=%D0%90%D0%B2%D1%82%D0%BE%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F_%D1%83%D1%80%D0%BE%D0%B2%D0%BD%D0%B5%D0%B9_%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D1%8F%D0%B4%D0%B0&diff=32730&oldid=prev 2025-10-10T16:28:45Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 19:28, 10 октября 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Строка 11:</td> <td colspan="2" class="diff-lineno">Строка 11:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\gamma_k}{\gamma_0}&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\gamma_k}{\gamma_0}&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">где </del>\<del style="font-weight: bold; text-decoration: none;">( </del>\<del style="font-weight: bold; text-decoration: none;">gamma_k </del>= \<del style="font-weight: bold; text-decoration: none;">text</del>{<del style="font-weight: bold; text-decoration: none;">Cov</del>}(<del style="font-weight: bold; text-decoration: none;">X_t, X_</del>{t<del style="font-weight: bold; text-decoration: none;">-</del>k}<del style="font-weight: bold; text-decoration: none;">) </del>\) <del style="font-weight: bold; text-decoration: none;">— автоковариационная функция, а </del>\<del style="font-weight: bold; text-decoration: none;">( \gamma_0 </del>= <del style="font-weight: bold; text-decoration: none;">\text</del>{<del style="font-weight: bold; text-decoration: none;">Var</del>}(<del style="font-weight: bold; text-decoration: none;">X_t) </del>\) <del style="font-weight: bold; text-decoration: none;">— дисперсия ряда</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=== Выборочная автокорреляционная функция ===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Для выборки временного ряда выборочный коэффициент автокорреляции вычисляется как:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;r_k = </ins>\<ins style="font-weight: bold; text-decoration: none;">frac{</ins>\<ins style="font-weight: bold; text-decoration: none;">sum_{t</ins>=<ins style="font-weight: bold; text-decoration: none;">1}^{n-k}(x_t - </ins>\<ins style="font-weight: bold; text-decoration: none;">bar</ins>{<ins style="font-weight: bold; text-decoration: none;">x</ins>}<ins style="font-weight: bold; text-decoration: none;">)</ins>(<ins style="font-weight: bold; text-decoration: none;">x_</ins>{t<ins style="font-weight: bold; text-decoration: none;">+</ins>k} <ins style="font-weight: bold; text-decoration: none;">- </ins>\<ins style="font-weight: bold; text-decoration: none;">bar{x}</ins>)<ins style="font-weight: bold; text-decoration: none;">}{</ins>\<ins style="font-weight: bold; text-decoration: none;">sum_{t</ins>=<ins style="font-weight: bold; text-decoration: none;">1}^</ins>{<ins style="font-weight: bold; text-decoration: none;">n</ins>}(<ins style="font-weight: bold; text-decoration: none;">x_t - </ins>\<ins style="font-weight: bold; text-decoration: none;">bar{x}</ins>)<ins style="font-weight: bold; text-decoration: none;">^2}&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=== Ряды с [[тренд]]ом ===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Временные ряды с трендом демонстрируют медленно убывающую автокорреляционную функцию, поскольку соседние наблюдения остаются похожими из-за общего направления изменения</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">В социально-экономическом моделировании автокорреляция может отражать:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Инерцию потребления: потребители медленно меняют привычки</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Ценовую память: цены зависят от предыдущих уровней</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Институциональную устойчивость: правила и нормы изменяются постепенно</ins></div></td></tr> </table>

Patarakin http://digida.mgpu.ru/index.php?title=%D0%90%D0%B2%D1%82%D0%BE%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F_%D1%83%D1%80%D0%BE%D0%B2%D0%BD%D0%B5%D0%B9_%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D1%8F%D0%B4%D0%B0&diff=32729&oldid=prev 2025-10-10T16:24:57Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 19:24, 10 октября 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10">Строка 10:</td> <td colspan="2" class="diff-lineno">Строка 10:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\gamma_k}{\gamma_0}&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\gamma_k}{\gamma_0}&lt;/math&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">где \( \gamma_k = \text{Cov}(X_t, X_{t-k}) \) — автоковариационная функция, а \( \gamma_0 = \text{Var}(X_t) \) — дисперсия ряда.</ins></div></td></tr> </table>

Patarakin http://digida.mgpu.ru/index.php?title=%D0%90%D0%B2%D1%82%D0%BE%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F_%D1%83%D1%80%D0%BE%D0%B2%D0%BD%D0%B5%D0%B9_%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D1%8F%D0%B4%D0%B0&diff=32728&oldid=prev 2025-10-10T16:24:23Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 19:24, 10 октября 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td> <td colspan="2" class="diff-lineno">Строка 6:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\text{Cov}(X_t, X_{t-k})}{\sqrt{\text{Var}(X_t) \cdot \text{Var}(X_{t-k})}}&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\rho_k = \frac{\text{Cov}(X_t, X_{t-k})}{\sqrt{\text{Var}(X_t) \cdot \text{Var}(X_{t-k})}}&lt;/math&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Для стационарного временного ряда автокорреляционная функция упрощается:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;\rho_k = \frac{\gamma_k}{\gamma_0}&lt;/math&gt;</ins></div></td></tr> </table>

Patarakin http://digida.mgpu.ru/index.php?title=%D0%90%D0%B2%D1%82%D0%BE%D0%BA%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F_%D1%83%D1%80%D0%BE%D0%B2%D0%BD%D0%B5%D0%B9_%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D1%8F%D0%B4%D0%B0&diff=32727&oldid=prev 2025-10-10T16:23:36Z

<p>Новая страница: «{{Понятие |Description=Автокорреляция уровней временного ряда (англ. autocorrelation of time series levels, серийная корреляция) — статистическая мера линейной зависимости между значениями временного ряда в различные моменты времени. Автокорреляция показывает, насколько т...»</p> <p><b>Новая страница</b></p><div>{{Понятие<br /> |Description=Автокорреляция уровней временного ряда (англ. autocorrelation of time series levels, серийная корреляция) — статистическая мера линейной зависимости между значениями временного ряда в различные моменты времени. Автокорреляция показывает, насколько текущее значение ряда связано с его предыдущими значениями на определенном временном лаге.<br /> |Field_of_knowledge=Экономика, Статистика<br /> }}<br /> Автокорреляция временного ряда \( \{X_t\} \) на лаге \( k \) определяется как коэффициент корреляции между \( X_t \) и \( X_{t-k} \):<br /> <br /> &lt;math&gt;\rho_k = \frac{\text{Cov}(X_t, X_{t-k})}{\sqrt{\text{Var}(X_t) \cdot \text{Var}(X_{t-k})}}&lt;/math&gt;</div>

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