{"id":37120,"date":"2021-02-15T19:32:01","date_gmt":"2021-02-15T18:32:01","guid":{"rendered":"https:\/\/datascientest.com\/?p=37120"},"modified":"2023-11-09T14:10:03","modified_gmt":"2023-11-09T14:10:03","slug":"arima-series-temporelles","status":"publish","type":"post","link":"https:\/\/datascientest.com\/arima-series-temporelles","title":{"rendered":"ARIMA : Mod\u00e8le de pr\u00e9diction des s\u00e9ries temporelles"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"37120\" class=\"elementor elementor-37120\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a811871 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a811871\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c8dc15f\" data-id=\"c8dc15f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-de3ac94 elementor-widget elementor-widget-heading\" data-id=\"de3ac94\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux s\u00e9ries temporelles, vous avez s\u00fbrement d\u00fb entendre parler de l\u2019ARIMA ou de l\u2019ARMA. En effet, ce sont les principaux processus utilis\u00e9s pour mod\u00e9liser des\u00a0s\u00e9ries temporelles\u00a0et ils constituent donc une notion fondamentale lorsque vous d\u00e9butez dans le domaine.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7c6c5fd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7c6c5fd\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bf4b967\" data-id=\"bf4b967\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-965dbc1 elementor-widget elementor-widget-text-editor\" data-id=\"965dbc1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><span style=\"font-weight: 400;\">Si vous ne savez pas encore ce qu\u2019est une s\u00e9rie temporelle, je vous conseille vivement d\u2019aller voir <\/span><strong><a href=\"https:\/\/datascientest.com\/series-temporelles\" target=\"_blank\" rel=\"noopener\">notre article sur les s\u00e9ries temporelles<\/a><\/strong><span style=\"font-weight: 400;\"> que nous avons publi\u00e9 sur le sujet car les notions qui y sont expos\u00e9es seront r\u00e9-utilis\u00e9es dans cet article.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9fbe3ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9fbe3ca\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ade4ba2\" data-id=\"ade4ba2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-939102a elementor-widget elementor-widget-text-editor\" data-id=\"939102a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;color: #000000\">Le processus ARIMA est une association de diff\u00e9rents de processus plus simples que nous allons expliquer dans cet article.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-701612a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"701612a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d33af3e\" data-id=\"d33af3e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d64a17d elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"d64a17d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Devenez un expert en Data Science<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a80f3b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a80f3b4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-712fdc5\" data-id=\"712fdc5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3293744 elementor-widget elementor-widget-heading\" data-id=\"3293744\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Le processus AR :\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-378dda4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"378dda4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fcac1c\" data-id=\"7fcac1c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d4f6f63 elementor-widget elementor-widget-text-editor\" data-id=\"d4f6f63\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000\"><span style=\"font-weight: 400\">Le p<\/span><\/span><span style=\"font-weight: 400\">rocessus AR signifie<\/span><b> autor\u00e9gressif<\/b><span style=\"font-weight: 400\">.<\/span><\/p><p><span style=\"font-weight: 400\">Concr\u00e8tement, si l\u2019on consid\u00e8re un processus stationnaire <\/span><span style=\"font-weight: 400\">X<\/span><span style=\"font-weight: 400\">t<\/span><span style=\"font-weight: 400\">, on consid\u00e8re qu\u2019il est autor\u00e9gressif d\u2019ordre p si l\u2019on peut <\/span><b style=\"color: #000000\">expliquer sa valeur \u00e0 l\u2019instant T en utilisant ses p termes pr\u00e9c\u00e9dents.<\/b><\/p><p><span style=\"font-weight: 400;color: #000000\">Math\u00e9matiquement, cela signifie que :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b386a9e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b386a9e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b9aaef7\" data-id=\"b9aaef7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db91acd elementor-widget elementor-widget-image\" data-id=\"db91acd\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"624\" height=\"67\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2.png\" class=\"attachment-large size-large wp-image-37136\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2.png 624w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2-300x32.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b4eae01 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b4eae01\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8a22b7c\" data-id=\"8a22b7c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3180f66 elementor-widget elementor-widget-text-editor\" data-id=\"3180f66\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000\"><span style=\"font-weight: 400\">avec <strong>\u03b5<\/strong> l\u2019erreur et <strong>(\ud835\udefc<\/strong><\/span><strong>1, \u2026,\ud835\udefcp) <\/strong><span style=\"font-weight: 400\"><strong>\u00a0<\/strong><\/span><span style=\"font-weight: 400\">des r\u00e9els<\/span><\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-81a66e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"81a66e9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1b1cb2f\" data-id=\"1b1cb2f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d45ef3a elementor-widget elementor-widget-heading\" data-id=\"d45ef3a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Le processus MA :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ee3be20 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ee3be20\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6ce7947\" data-id=\"6ce7947\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bd770da elementor-widget elementor-widget-text-editor\" data-id=\"bd770da\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000\"><span style=\"font-weight: 400\">MA signifie \u2018moving average\u2019 ou en fran\u00e7ais <\/span><\/span><b>moyenne mobile<\/b><span style=\"font-weight: 400\">.<\/span><\/p><p><span style=\"font-weight: 400\">Soit X<\/span><span style=\"font-weight: 400\">t <\/span><span style=\"font-weight: 400\">\u00a0une s\u00e9rie temporelle, on consid\u00e8re que c\u2019est un processus MA d\u2019ordre p si on peut exprimer sa valeur \u00e0 l\u2019instant t comme une combinaison lin\u00e9aire d\u2019erreur al\u00e9atoires (bruit blanc).<\/span><\/p><p><span style=\"font-weight: 400;color: #000000\">Math\u00e9matiquement on traduit cela par :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-83182b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"83182b4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e870e24\" data-id=\"e870e24\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5024fca elementor-widget elementor-widget-image\" data-id=\"5024fca\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"512\" height=\"55\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-3-1.png\" class=\"attachment-large size-large wp-image-37146\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-3-1.png 512w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-3-1-300x32.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3483f32 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3483f32\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-33aedf5\" data-id=\"33aedf5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-71333aa elementor-widget elementor-widget-text-editor\" data-id=\"71333aa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000\"><span style=\"font-weight: 400\">avec <\/span><span style=\"font-weight: 400\"><strong>\u03b5<\/strong> l\u2019erreur et (\ud835\udefc<\/span><span style=\"font-weight: 400\">1<\/span><span style=\"font-weight: 400\">, \u2026,\ud835\udefc<\/span><span style=\"font-weight: 400\">p<\/span><span style=\"font-weight: 400\">) <\/span><span style=\"font-weight: 400\">\u00a0\u00a0<\/span><span style=\"font-weight: 400\">des r\u00e9els<\/span><\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cd6afb1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cd6afb1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7020439\" data-id=\"7020439\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dd4e03e elementor-widget elementor-widget-heading\" data-id=\"dd4e03e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Le processus ARMA :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-84610c3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"84610c3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fecb870\" data-id=\"fecb870\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c32b2bd elementor-widget elementor-widget-text-editor\" data-id=\"c32b2bd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Comme vous vous en doutez, le mod\u00e8le ARMA est tout simplement une combinaison d\u2019un processus AR et d\u2019un processus MA. <\/span><b>Cela permet de mod\u00e9liser des s\u00e9ries temporelles plus complexes.<\/b><\/p><p><span style=\"font-weight: 400\"><span style=\"color: #000000\">Un mod\u00e8le ARMA d\u2019ordre (p,q) s\u2019\u00e9crit donc sous la forme :<\/span> <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3e0f395 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e0f395\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1ed15c5\" data-id=\"1ed15c5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-de3b5bc elementor-widget elementor-widget-image\" data-id=\"de3b5bc\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"624\" height=\"67\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/02\/ARIMA.png\" class=\"attachment-large size-large wp-image-53235\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/02\/ARIMA.png 624w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/02\/ARIMA-300x32.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-86bad5b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"86bad5b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2d759b5\" data-id=\"2d759b5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b274d8c elementor-widget elementor-widget-text-editor\" data-id=\"b274d8c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000\"><span style=\"font-weight: 400\">Avec <\/span><span style=\"font-weight: 400\">(\ud835\udefc<\/span><span style=\"font-weight: 400\">1<\/span><span style=\"font-weight: 400\">, \u2026,\ud835\udefc<\/span><span style=\"font-weight: 400\">p<\/span><span style=\"font-weight: 400\">) <\/span><span style=\"font-weight: 400\">\u00a0<\/span><span style=\"font-weight: 400\">\u00a0et <\/span><span style=\"font-weight: 400\">(\ud835\udefd<\/span><span style=\"font-weight: 400\">1<\/span><span style=\"font-weight: 400\">, \u2026,\ud835\udefd<\/span><span style=\"font-weight: 400\">q<\/span><span style=\"font-weight: 400\">)<\/span><span style=\"font-weight: 400\"> des r\u00e9els.<\/span><\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b8abfd9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b8abfd9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fbc9a7\" data-id=\"7fbc9a7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db765fc elementor-widget elementor-widget-text-editor\" data-id=\"db765fc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Cependant, l\u2019une des limitations de ce mod\u00e8le est qu\u2019<strong><span style=\"color: #000000\">il ne peut mod\u00e9liser que des s\u00e9ries temporelles stationnaires.\u00a0<\/span><\/strong><\/p><p>Ainsi, il ne peut mod\u00e9liser une s\u00e9rie temporelle avec <strong>une tendance lin\u00e9aire croissante<\/strong>. C\u2019est pour pallier ce probl\u00e8me que le mod\u00e8le ARIMA a \u00e9t\u00e9 d\u00e9velopp\u00e9<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3ba15d5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3ba15d5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2789c7c\" data-id=\"2789c7c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ca5ede9 elementor-widget elementor-widget-image\" data-id=\"ca5ede9\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"409\" height=\"268\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1-1.png\" class=\"attachment-large size-large wp-image-37218\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1-1.png 409w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1-1-300x197.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Exemples de processus AR : Source Wikip\u00e9dia<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5368f8d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5368f8d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bfd9fe8\" data-id=\"bfd9fe8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1e89cde elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"1e89cde\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">En savoir plus sur la formation de Data Scientist<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5ff519c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5ff519c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1011f79\" data-id=\"1011f79\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6fd4937 elementor-widget elementor-widget-heading\" data-id=\"6fd4937\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Le mod\u00e8le ARIMA :\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7df1208 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7df1208\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2b3e2f6\" data-id=\"2b3e2f6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f9522c8 elementor-widget elementor-widget-text-editor\" data-id=\"f9522c8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;color: #000000\">Le I du mod\u00e8le ARIMA signifie \u2018integrated\u2019 pour int\u00e9gration. En diff\u00e9renciant les s\u00e9ries temporelles, il est possible de retirer les tendances qu\u2019elles pr\u00e9sentent pour les stationnariser.<\/span><\/p><p><span style=\"font-weight: 400;color: #000000\">Prenons l\u2019exemple d\u2019une s\u00e9rie temporelle avec une tendance lin\u00e9aire de la forme :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1c897ea elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1c897ea\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-929874f\" data-id=\"929874f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3fec372 elementor-widget elementor-widget-image\" data-id=\"3fec372\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"624\" height=\"31\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2-1.png\" class=\"attachment-large size-large wp-image-37219\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2-1.png 624w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-2-1-300x15.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ff1af01 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ff1af01\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c3492c8\" data-id=\"c3492c8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a0a3415 elementor-widget elementor-widget-image\" data-id=\"a0a3415\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"624\" height=\"31\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaaaaaa.png\" class=\"attachment-large size-large wp-image-37222\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaaaaaa.png 624w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaaaaaa-300x15.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d8a7949 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d8a7949\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d5158da\" data-id=\"d5158da\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e8103bf elementor-widget elementor-widget-text-editor\" data-id=\"e8103bf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Ainsi en diff\u00e9renciant la s\u00e9rie une fois , la d\u00e9pendance temporelle lin\u00e9aire est \u00e9limin\u00e9e et la <\/span><b>diff\u00e9rence est stationnaire<\/b><span style=\"font-weight: 400\">.<\/span><\/p><p><span style=\"font-weight: 400\">De la m\u00eame fa\u00e7on, une tendance quadratique peut \u00eatre \u00e9limin\u00e9e en diff\u00e9renciant la s\u00e9rie deux fois.<\/span><\/p><p><span style=\"font-weight: 400\">Une fois la s\u00e9rie stationnaris\u00e9e, il est alors possible\u00a0 d\u2019appliquer le mod\u00e8le ARMA.<\/span><\/p><p><b>Le mod\u00e8le ARIMA est donc une combinaison de ce processus de diff\u00e9renciation et du processus ARMA classique.<\/b><\/p><p><span style=\"font-weight: 400\">Par ailleurs, si la s\u00e9rie temporelle pr\u00e9sente \u00e0 la fois une tendance et une saisonnalit\u00e9, il est possible d\u2019utiliser le mod\u00e8le <\/span><b>SARIMA<\/b><span style=\"font-weight: 400\"> qui est un mod\u00e8le ARIMA prenant aussi en compte une composante saisonni\u00e8re.<\/span><\/p><p><span style=\"font-weight: 400\">\u00a0<\/span><b>Et en pratique \u00e7a donne quoi ?<\/b><\/p><p><span style=\"font-weight: 400\">On cherche \u00e0 pr\u00e9dire le nombre de passagers mensuels d\u2019une compagnie a\u00e9rienne dont on a les donn\u00e9es entre 1949 et 1960, Disponible sur Kaggle\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e9deee8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e9deee8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-669e720\" data-id=\"669e720\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0f983e2 elementor-widget elementor-widget-image\" data-id=\"0f983e2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"381\" height=\"249\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-4-1.png\" class=\"attachment-large size-large wp-image-37232\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-4-1.png 381w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-4-1-300x196.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a9f8037 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a9f8037\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a75ca4c\" data-id=\"a75ca4c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cb8cf3b elementor-widget elementor-widget-text-editor\" data-id=\"cb8cf3b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">En utilisant la fonction SARIMAX de la biblioth\u00e8que <\/span><b><i>statsmodels<\/i><\/b><span style=\"font-weight: 400\">, il est possible de pr\u00e9dire la s\u00e9rie temporelle sur les 15 prochains mois. On choisit de prendre un processus AR d\u2019ordre 1, un processus MA d\u2019ordre 1, une diff\u00e9renciation d\u2019ordre 1 et une saisonnalit\u00e9 sur 12 mois.<\/span><\/p><p><span style=\"font-weight: 400\">Par ailleurs, le mod\u00e8le permet de calculer un intervalle de confiance de 95% de la pr\u00e9diction affich\u00e9 ici en gris<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c3540c8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c3540c8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d8de308\" data-id=\"d8de308\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f369961 elementor-widget elementor-widget-image\" data-id=\"f369961\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"512\" height=\"180\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-5.png\" class=\"attachment-large size-large wp-image-37234\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-5.png 512w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/unnamed-5-300x105.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b3aada6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b3aada6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6059c55\" data-id=\"6059c55\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ada4303 elementor-widget elementor-widget-heading\" data-id=\"ada4303\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1fd04c1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1fd04c1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8e415e8\" data-id=\"8e415e8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4cf3c0a elementor-widget elementor-widget-text-editor\" data-id=\"4cf3c0a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;color: #000000\">Plus r\u00e9cemment les r\u00e9seaux de neurones sont devenus de plus en plus utilis\u00e9s pour la pr\u00e9diction des s\u00e9ries temporelles car ils viennent corriger certains d\u00e9fauts des m\u00e9thodes \u2018classiques\u2019 comme l\u2019ARIMA. D\u00e9couvrez en plus sur les r\u00e9seaux de neurones en suivant l\u2019une de nos formations.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9d03685 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9d03685\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-733b766\" data-id=\"733b766\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ce32e8f elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"ce32e8f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Devenez Data Scientist<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9bad741 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9bad741\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-87f13b0\" data-id=\"87f13b0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6dd9146 elementor-widget elementor-widget-html\" data-id=\"6dd9146\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script>\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Quel est le processus AR ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Le processus AR signifie autor\u00e9gressif. Concr\u00e8tement si l\u2019on consid\u00e8re un processus stationnaire Xt , on consid\u00e8re qu\u2019il est autor\u00e9gressif d\u2019ordre p si l\u2019on peut expliquer sa valeur \u00e0 l\u2019instant t en utilisant ses p termes pr\u00e9c\u00e9dents.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Quel est le processus MA ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"MA signifie \u2018moving average\u2019 ou en fran\u00e7ais moyenne mobile. Soit Xt  une s\u00e9rie temporelle, on consid\u00e8re que c\u2019est un processus MA d\u2019ordre p si on peut exprimer sa valeur \u00e0 l\u2019instant t comme une combinaison lin\u00e9aire d\u2019erreur al\u00e9atoires (bruit blanc).\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Qu'est-ce que le processus ARMA ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Comme vous vous en doutez, le mod\u00e8le ARMA est tout simplement une combinaison d\u2019un processus AR et d\u2019un processus MA. Cela permet de mod\u00e9liser des s\u00e9ries temporelles plus complexes.\"\n    }\n  }]\n}\n<\/script>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux s\u00e9ries temporelles, vous avez s\u00fbrement d\u00fb entendre parler de l\u2019ARIMA ou de l\u2019ARMA. En effet, ce sont les principaux processus utilis\u00e9s pour mod\u00e9liser des&nbsp;s\u00e9ries temporelles&nbsp;et ils constituent donc une notion fondamentale lorsque vous d\u00e9butez dans le domaine. Si vous ne savez pas encore ce qu\u2019est une s\u00e9rie temporelle, [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":44233,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ARIMA : Mod\u00e8le de pr\u00e9diction des s\u00e9ries temporelles<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez les cas d&#039;usage de l\u2019ARIMA : principaux processus utilis\u00e9s pour mod\u00e9liser des s\u00e9ries temporelles, tr\u00e8s importantes en Data Science.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/arima-series-temporelles\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ARIMA : Mod\u00e8le de pr\u00e9diction des s\u00e9ries temporelles\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/arima-series-temporelles\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2021-02-15T18:32:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T14:10:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/illu_arima_blog-87.png\" \/>\n\t<meta property=\"og:image:width\" content=\"4268\" \/>\n\t<meta property=\"og:image:height\" content=\"2342\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Raphael Kassel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raphael Kassel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/arima-series-temporelles\",\"url\":\"https:\/\/datascientest.com\/arima-series-temporelles\",\"name\":\"ARIMA : Mod\u00e8le de pr\u00e9diction des s\u00e9ries temporelles\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2021-02-15T18:32:01+00:00\",\"dateModified\":\"2023-11-09T14:10:03+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"D\u00e9couvrez les cas d'usage de l\u2019ARIMA : principaux processus utilis\u00e9s pour mod\u00e9liser des s\u00e9ries temporelles, tr\u00e8s importantes en Data Science.\",\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/arima-series-temporelles\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/#website\",\"url\":\"https:\/\/datascientest.com\/\",\"name\":\"Formation Data Science | DataScientest.com\",\"description\":\"Leader de la formation en Data Science\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\",\"name\":\"Raphael Kassel\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"contentUrl\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"caption\":\"Raphael Kassel\"},\"description\":\"Raphael Kassel est le Head of Data Programs chez DataScientest. 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