{"id":146078,"date":"2023-09-18T07:30:00","date_gmt":"2023-09-18T07:30:00","guid":{"rendered":"https:\/\/datascientest.com\/?p=146078"},"modified":"2023-11-09T13:43:10","modified_gmt":"2023-11-09T13:43:10","slug":"le-modele-var","status":"publish","type":"post","link":"https:\/\/datascientest.com\/le-modele-var","title":{"rendered":"Le mod\u00e8le VAR : de l\u2019approche m\u00e9tier au plotting des r\u00e9sultats"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"146078\" class=\"elementor elementor-146078\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a7e5ba3 e-flex e-con-boxed e-con\" data-id=\"a7e5ba3\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d91432b elementor-widget elementor-widget-text-editor\" data-id=\"d91432b\" 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<ol><li><a href=\"#introduction\">Introduction<\/a><\/li><li><a href=\"#definition\">D\u00e9finition du mod\u00e8le VAR : \u00e9quation &amp; int\u00e9r\u00eat<\/a><\/li><li><a href=\"#import\">Import des libraires, set-up<\/a><\/li><li><a href=\"#stationnarite\">La stationnarit\u00e9 : kezako et pourquoi c\u2019est important<\/a><\/li><li><a href=\"#modele\">Le mod\u00e8le et la convergence lag\/variables<\/a><br \/>a. <a href=\"#Selectionner_des_variables\">S\u00e9lectionner des variables<\/a><br \/>b. <a href=\"#Selection_du_lag_optimal\">S\u00e9lection du lag optimal<\/a><\/li><li><a href=\"#prediction\">Pr\u00e9diction avec le meilleur mod\u00e8le et affichage des r\u00e9sultats<\/a><\/li><li><a href=\"#Conclusion\">Conclusion<\/a><\/li><\/ol>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c99ad21 elementor-widget elementor-widget-menu-anchor\" data-id=\"c99ad21\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\nbody.elementor-page .elementor-widget-menu-anchor{margin-bottom:0}<\/style>\t\t<div id=\"introduction\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9efe730 e-flex e-con-boxed e-con\" data-id=\"9efe730\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c3e56e7 elementor-widget elementor-widget-heading\" data-id=\"c3e56e7\" 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><h3 class=\"elementor-heading-title elementor-size-default\">1. Introduction<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a46865 elementor-widget elementor-widget-text-editor\" data-id=\"2a46865\" 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;\">Bienvenue sur cet article explicatif du mod\u00e8le VAR. Nous \u00e9tudierons les \u201cbases\u201d concernant ce mod\u00e8le mais pas celles g\u00e9n\u00e9rales \u00e0 propos des s\u00e9ries temporelles (en dehors de la stationnarit\u00e9 \ud83e\udd2f).\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Le dataset utilis\u00e9 est disponible <a href=\"https:\/\/www.kaggle.com\/datasets\/albertovidalrod\/electricity-consumption-uk-20092022?select=historic_demand_2009_2023_noNaN.csv\">ici<\/a>. Et voici mon github : <a href=\"https:\/\/github.com\/gambitl\/Article_VAR_FR_Public\">https:\/\/github.com\/gambitl\/Article_VAR_FR_Public<\/a><\/span><\/p><p><span style=\"font-weight: 400;\">\u00c0 la fin de cette article, vous saurez :\u00a0<\/span><\/p><ul><li><span style=\"font-weight: 400;\">Ce qu\u2019est le mod\u00e8le VAR et quel est son int\u00e9r\u00eat \ud83e\uddd0<\/span><\/li><li>Comment et pourquoi pr\u00e9parer son <a href=\"https:\/\/datascientest.com\/dataset-definition\">dataset<\/a> pour utiliser le mod\u00e8le VAR<\/li><li>Comment choisir le bon param\u00e8tre (nombre de lag) selon son dataset pour minimiser une m\u00e9trique d\u2019erreur et pas simplement une m\u00e9trique statistique<\/li><li>Pourquoi et comment tester le lien entre les variables et enlever celles qui bruitent le mod\u00e8le<\/li><li>Automatiser les deux \u00e9tapes pr\u00e9c\u00e9dentes et converger vers un r\u00e9sultat optimal qui combine le param\u00e8tre le plus performant et le jeu de donn\u00e9es le plus adapt\u00e9 \ud83d\udc4d<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e88c345 elementor-widget elementor-widget-text-editor\" data-id=\"e88c345\" 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;\">\u00c0 chaque \u00e9tape, je mettrais d\u2019abord en avant les points th\u00e9oriques, puis les fonctions \u00ab\u00a0maisons\u00a0\u00bb, et enfin le code qui appelle les fonctions. Chaque fonction est assez comment\u00e9e et expliqu\u00e9e au sein m\u00eame du code.<\/span><\/p><p><span style=\"font-weight: 400;\">Vous trouverez \u00e0 la fin de l\u2019article l\u2019ensemble du code hors fonction.<\/span><\/p><p><span style=\"font-weight: 400;\">Dans le cas de cet exemple, j\u2019utilise le mod\u00e8le VAR pour pr\u00e9dire UNE variable en particulier.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b4e1a2 elementor-widget elementor-widget-menu-anchor\" data-id=\"6b4e1a2\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"definition\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-bce13a4 e-flex e-con-boxed e-con\" data-id=\"bce13a4\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-566482d elementor-widget elementor-widget-heading\" data-id=\"566482d\" 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\">2. D\u00e9finition du mod\u00e8le VAR : \u00e9quation & int\u00e9r\u00eat<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-af0278a elementor-widget elementor-widget-text-editor\" data-id=\"af0278a\" 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;\">Le mod\u00e8le VAR pour Vector Autoregression est un mod\u00e8le de s\u00e9ries temporelles qui permet de pr\u00e9dire plusieurs variables dans le temps. Chacune des pr\u00e9dictions de chaque variable contribue \u00e0 la pr\u00e9diction des autres. Ainsi, si on l\u2019\u00e9crivait sous un format lin\u00e9aire, nous aurions ceci\u00a0:<\/span><\/p><p><span style=\"font-weight: 400;\">Soit 2 variables, Y et X, et (t) un moment dans le temps.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Y(t+1) = f(Y(t), X(t))\u00a0<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">X(t+1) = f(X(t), Y(t))<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Y(t+1) = \u03b11 + \u03b21Y(t) + \u03b22X(t) + \u03b51<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">X(t+1) = \u03b12 + \u03b23X(t) + \u03b24Y(t) + \u03b52<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59da2bb elementor-widget elementor-widget-text-editor\" data-id=\"59da2bb\" 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;\">Avec \u03b1 les constantes, \u03b2 les coefficients associ\u00e9s aux variables, \u03b5 les erreurs.<\/span><\/p><p><span style=\"font-weight: 400;\">Le mod\u00e8le calcule sur la base de l\u2019historique les constantes, coefficients pour chaque variable<\/span><\/p><p><span style=\"font-weight: 400;\">De plus, le mod\u00e8le inclut des \u00ab\u00a0lags\u00a0\u00bb (\u03bb), qui permettent d\u2019inclure dans le calcul de X(t+1), Y(t+1) toutes les valeurs de X, Y jusqu\u2019\u00e0 X(t- \u03bb), Y(t- \u03bb). Dans le syst\u00e8me pr\u00e9c\u00e9dent, la valeur suivante de la variable (X) est calcul\u00e9e en fonction de la valeur pr\u00e9c\u00e9dente de (X) et de la valeur pr\u00e9c\u00e9dente de (Y). Le lag (\u03bb) est donc \u00e9gal \u00e0 1.<\/span><\/p><p><span style=\"font-weight: 400;\">Ce sont ces lags qui constituent le param\u00e8tre \u00e0 optimiser dans ce mod\u00e8le, c\u2019est-\u00e0-dire combien de jours d\u2019historique vont composer nos \u00e9quations.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c25972b elementor-widget elementor-widget-menu-anchor\" data-id=\"c25972b\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"import\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-31f1af4 e-flex e-con-boxed e-con\" data-id=\"31f1af4\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-90e82a3 elementor-widget elementor-widget-heading\" data-id=\"90e82a3\" 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\">3. Import des libraires, set-up<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-74ef664 elementor-widget elementor-widget-text-editor\" data-id=\"74ef664\" 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;\">Nous avons besoin des imports suivants : <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1835d40 elementor-widget elementor-widget-code-highlight\" data-id=\"1835d40\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>import pandas as pd\r\nimport numpy as np\r\nfrom sklearn.model_selection import TimeSeriesSplit\r\nfrom sklearn.metrics import r2_score, mean_absolute_error, mean_squared_error\r\nfrom sklearn.preprocessing import MinMaxScaler\r\nimport seaborn as sns\r\nimport matplotlib.pyplot as plt\r\nimport matplotlib as mpl\r\nfrom statsmodels.tsa.vector_ar.var_model import VAR\r\nfrom statsmodels.tsa.stattools import grangercausalitytests, adfuller\r\nfrom scipy.stats import boxcox, norm, probplot, normaltest\r\nfrom scipy.special import inv_boxcox<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3a8e182 elementor-widget elementor-widget-text-editor\" data-id=\"3a8e182\" 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;\">Chargement de la donn\u00e9e :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1edb7ea elementor-widget elementor-widget-code-highlight\" data-id=\"1edb7ea\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df = pd.read_csv(\"path.csv\")\r\ndf['settlement_date'] = pd.to_datetime(df['settlement_date'])\r\ndf = df.set_index('settlement_date')\r\ndf = df.drop(['settlement_period', 'period_hour'], axis = 1)\r\nexog = df[['is_holiday']].copy()\r\ndf = df.drop(['is_holiday'], axis =1)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-417789b elementor-widget elementor-widget-text-editor\" data-id=\"417789b\" 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;\">Param\u00e8tres :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3044ff1 elementor-widget elementor-widget-code-highlight\" data-id=\"3044ff1\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>target_variable = \"tsd\" #the feature we ultimately want to predict\r\nn_period_predict = 48 * 7 #the number of period we want to predict. I want to predict 7 days and there are 48 data points per day<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a910857 elementor-widget elementor-widget-text-editor\" data-id=\"a910857\" 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;\">Pr\u00e9parations\/Cleaning : <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-41f6172 elementor-widget elementor-widget-code-highlight\" data-id=\"41f6172\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>mask = (df.index > '2022-01-01') #I will use the data post 2022\r\ndf_pour_var = df.loc[mask]\r\nexog_pour_var = exog.loc[mask]\r\ndf_pour_var = df_pour_var +1 #We erase the every value that are equals to 0 in order to facilitate the boxcox transformation\r\ninitial_testing_set = df_pour_var[-n_period_predict:] #there will be a lot of transformation so we want to keep a safe testing set<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-847ea52 elementor-widget elementor-widget-menu-anchor\" data-id=\"847ea52\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"stationnarite\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8058c4f e-flex e-con-boxed e-con\" data-id=\"8058c4f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3ea9b67 elementor-widget elementor-widget-heading\" data-id=\"3ea9b67\" 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\">4. La stationnarit\u00e9 : kezako et pourquoi c\u2019est important<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9bde8c7 elementor-widget elementor-widget-text-editor\" data-id=\"9bde8c7\" 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;\">On d\u00e9finit la stationnarit\u00e9 (faible) de la mani\u00e8re suivante\u00a0:<\/span><\/p><ul><li><span style=\"font-weight: 400;\">Quelque soit le moment (t) dans le temps, l\u2019esp\u00e9rance de notre variable est toujours la m\u00eame. Il y a absence de tendance.<\/span><\/li><li><span style=\"font-weight: 400;\">Quelque soit le moment (t) dans le temps, la variance de notre variable est toujours la m\u00eame et non infinie.<\/span><\/li><li><span style=\"font-weight: 400;\">Quelque soit le moment dans le temps, l\u2019auto-corr\u00e9lation entre deux moments dans le temps n\u2019est fonction que du d\u00e9calage dans le temps (et la position ne change pas la valeur de l\u2019auto-corr\u00e9lation).<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Sans rentrer dans les d\u00e9tails, il a \u00e9t\u00e9 montr\u00e9 que r\u00e9aliser une r\u00e9gression sur une variable non stationnaire m\u00eame \u00e0 des param\u00e8tres invalides (ils suivent un mouvement brownien c\u2019est-\u00e0-dire tr\u00e8s irr\u00e9gulier, pour simplifier). Je recommande <a href=\"https:\/\/www.researchgate.net\/post\/Why-stationary-is-basic-assumption-for-Time-series-analysis\">ce feed sur researchgate<\/a> pour plus de d\u00e9tails.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f0f4e2f elementor-widget elementor-widget-text-editor\" data-id=\"f0f4e2f\" 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;\">La premi\u00e8re \u00e9tape lorsqu&rsquo;on r\u00e9alise un mod\u00e8le de s\u00e9ries temporelles est donc de stationnariser notre s\u00e9rie. Pour cela, il existe plusieurs m\u00e9thodes, qui consiste \u00e0 transformer les donn\u00e9es :\u00a0<\/span><\/p><ul><li><span style=\"font-weight: 400;\">Les diff\u00e9rentes m\u00e9thodes de transformation pour normaliser notre donn\u00e9e, comme MinMaxScaler()<\/span><\/li><li><span style=\"font-weight: 400;\">La <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Transform%C3%A9e_de_Box-Cox\">transformation Boxcox<\/a>, tr\u00e8s utilis\u00e9e et commune dans le cas des s\u00e9ries temporelles.<\/span><\/li><li>La diff\u00e9renciation, qui consiste \u00e0 soustraire \u00e0 une valeur de la s\u00e9rie sa valeur pr\u00e9c\u00e9dente. C\u2019est une m\u00e9thode tr\u00e8s efficace, il est rare (de mon exp\u00e9rience) qu\u2019une s\u00e9rie ne soit pas stationnaire apr\u00e8s une, ou deux diff\u00e9renciation.\u00a0 A noter que dans des mod\u00e8les <a href=\"https:\/\/datascientest.com\/arima-series-temporelles\">ARIMA<\/a>\/ARMA, en g\u00e9n\u00e9ral, la librairie s\u2019occupe elle m\u00eame de diff\u00e9rencier la s\u00e9rie. mais ce n\u2019est pas le cas ici \ud83d\ude00<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fce1b71 elementor-widget elementor-widget-text-editor\" data-id=\"fce1b71\" 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;\">Dans l\u2019id\u00e9al, on souhaite transformer une s\u00e9rie gr\u00e2ce \u00e0 Boxcox, puis la diff\u00e9rencier si besoin. <\/span><\/p><p><span style=\"font-weight: 400;\">Malheureusement, toutes les s\u00e9ries ne se transforment pas via Boxcox (valeurs n\u00e9gatives). Je vous propose donc le code suivant qui va tester l\u2019ensemble : <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8afec2e elementor-widget elementor-widget-code-highlight\" data-id=\"8afec2e\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def box_cox_test(dataframe_to_test):\r\n    \"\"\"_summary_\r\n\r\n\r\n    Args:\r\n        dataframe_to_test (dataframe)\r\n\r\n\r\n    Returns:\r\n        list_box_cox : the list of values you can transform thanks to boxcox\r\n        list_non_box_cox : the list of values you CAN'T transform thanks to boxcox\r\n    \"\"\"\r\n    list_non_transformed = []\r\n    list_box_cox = []\r\n    for col in dataframe_to_test:\r\n        data = dataframe_to_test[col]\r\n        if (data < 0).values.any():\r\n            list_non_transformed.append(col)\r\n            continue\r\n        fig = plt.figure()\r\n        ax1 = fig.add_subplot(221)\r\n        prob = probplot(data, dist=norm, plot=ax1)\r\n        ax1.set_xlabel('')\r\n        ax1.set_title('Probplot against normal distribution')\r\n\r\n\r\n        ax21 = fig.add_subplot(222)\r\n        ax21.hist(data)\r\n        ax21.set_xlabel(col)\r\n        ax21.set_title('distplot')\r\n\r\n\r\n        # normality test\r\n        stat, p = normaltest(data)\r\n        print('Statistics=%.3f, p=%.3f' % (stat, p))\r\n        # interpret\r\n        alpha = 0.05\r\n        if p > alpha:\r\n            print('Sample looks Gaussian (fail to reject H0)')\r\n        else:\r\n            print('Sample does not look Gaussian (reject H0)')\r\n\r\n\r\n        xt, _ = boxcox(data)\r\n        if not np.isfinite(xt).any():\r\n            list_non_transformed.append(col)\r\n            continue\r\n        list_box_cox.append(col)\r\n       \r\n        ax2 = fig.add_subplot(223)\r\n        prob = probplot(xt, dist=norm, plot=ax2)\r\n        ax2.set_title('Probplot after Box-Cox transformation')\r\n        ax22 = fig.add_subplot(224)\r\n        ax22.hist(xt)\r\n        ax22.set_xlabel(col)\r\n        ax22.set_title('distplot')\r\n\r\n\r\n        stat, p = normaltest(xt)\r\n        print('Statistics=%.3f, p=%.3f' % (stat, p))\r\n        # interpret\r\n        alpha = 0.05\r\n        if p > alpha:\r\n            print('Sample looks Gaussian (fail to reject H0)')\r\n        else:\r\n            print('Sample does not look Gaussian (reject H0)')\r\n       \r\n        plt.subplots_adjust(top = 0.99, bottom=0.01, hspace=1.2, wspace=0.4)\r\n        plt.show()\r\n    print('*'*50 +'\\n' +'*'*50)\r\n    print(f\"Les donn\u00e9es suivantes n'ont pas pu \u00eatre scaled (n\u00e9gatives, infinites) : {list_non_transformed}. \\n Voici leur plot non transform\u00e9\")\r\n    for col in list_non_transformed:\r\n        data = dataframe_to_test[col]\r\n        fig = plt.figure()\r\n        ax1 = fig.add_subplot(211)\r\n        prob = probplot(data, dist=norm, plot=ax1)\r\n        ax1.set_xlabel('')\r\n        ax1.set_title('Probplot against normal distribution')\r\n\r\n\r\n        ax21 = fig.add_subplot(212)\r\n        ax21.hist(data)\r\n        ax21.set_xlabel(col)\r\n        ax21.set_title('distplot')\r\n\r\n\r\n    return list_box_cox, list_non_transformed<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ba8620 elementor-widget elementor-widget-text-editor\" data-id=\"8ba8620\" 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;\">On l\u2019utilise pour tester notre dataframe :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d819139 elementor-widget elementor-widget-code-highlight\" data-id=\"d819139\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>list_features_to_box_cox, list_features_non_box_cox = box_cox_test(df_pour_var)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-77f5589 elementor-widget elementor-widget-text-editor\" data-id=\"77f5589\" 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;\">Nous avons donc maintenant une liste de variables qui peuvent \u00eatre transform\u00e9es via boxcox, et une liste qui ne peut pas \u00eatre transform\u00e9es via boxcox.<\/span><\/p><p><span style=\"font-weight: 400;\">Nous transformons donc les variables qui peuvent l\u2019\u00eatre via box cox. J\u2019ai cod\u00e9 une fonction pour obtenir un dictionnaire qui contient les associations \u00ab\u00a0features &#8211; lambda\u00a0\u00bb utilis\u00e9es pour la transformation. Cela va nous servir pour la suite !<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-336809e elementor-widget elementor-widget-code-highlight\" data-id=\"336809e\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def transfo_boxcox(dataframe_to_transform, list_features_to_transform):\r\n    \"\"\"_summary_\r\n    Args:\r\n        dataframe_to_transform (dataframe)\r\n        list_features_to_transform (list)\r\n    Returns:\r\n        transformed (dataframe): the dataframe after being transformed\r\n        dict_lambda(dict): the dict containing in key the name of a feature and in value the lambda used for transforming it via boxcox\r\n    \"\"\"\r\n    dict_lambda = {}\r\n    transformed = dataframe_to_transform.copy()\r\n    for ft in list_features_to_transform:\r\n        transformed[ft], l = boxcox(dataframe_to_transform[ft])\r\n        dict_lambda[ft] = l\r\n    return transformed, dict_lambda<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4cc4b4b elementor-widget elementor-widget-code-highlight\" data-id=\"4cc4b4b\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_var_transformed, dict_lambda_bc = transfo_boxcox(df_pour_var, list_features_to_box_cox)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8503dcb elementor-widget elementor-widget-code-highlight\" data-id=\"8503dcb\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>#We apply a minmaxscaler transform to the data we could not transform thanks to boxcox\r\nminmaxscaler = MinMaxScaler()\r\nminmaxscaler = minmaxscaler.fit(df_pour_var[list_features_non_box_cox])\r\ndf_var_transformed[list_features_non_box_cox] = minmaxscaler.transform(df_pour_var[list_features_non_box_cox])<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c26bedb elementor-widget elementor-widget-text-editor\" data-id=\"c26bedb\" 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;\">Il est temps de tester nos features et de savoir si elles sont stationnaires. <\/span><span style=\"font-weight: 400;\">Voici la fonction de test :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f71a63d elementor-widget elementor-widget-code-highlight\" data-id=\"f71a63d\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def dickey_fuller_test(data, seuil_signif=0.05, name='', verbose=False):\r\n    \"\"\"A function tests whether our features are stationary or not.\r\n\r\n\r\n    Args:\r\n        data (series): the data to test\r\n        seuil_signif (float, optional): test level. Defaults to 0.05.\r\n        name (str, optional): _description_. Defaults to ''.\r\n        verbose (bool, optional): _description_. Defaults to False.\r\n    \"\"\"\r\n    result = adfuller(data, autolag='AIC')\r\n    output = {'Test statistic':round(result[0], 4), 'p_value':round(result[1], 4), 'n_lags':round(result[2], 4), 'n_obs':result[3]}\r\n    p_value = output['p_value']\r\n\r\n\r\n    # Print Summary\r\n    print(f'    Augmented Dickey-Fuller test on : \"{name}\"', \"\\n   \", '~'*47)\r\n    print(f' H0: the data shows a unit root, and then is not stationary.')\r\n    print(f' P-Value equals      : {p_value}')\r\n    print(f' Confidence level    = {seuil_signif}')\r\n    print(f' Test statistic   = {output[\"Test statistic\r\n\"]}')\r\n    print(f' Number of lags = {output[\"n_lags\"]}')\r\n\r\n\r\n    if p_value <= seuil_signif:\r\n        print(f\" => P-Value = {p_value} <= {seuil_signif}. We can reject H0 on the confidence level.\")\r\n        print(f\" => The serie is stationary.\")\r\n    else:\r\n        print(f\" => P-Value = {p_value} > {seuil_signif}. We can not reject H0 on the confidence level.\")\r\n        print(f\" => The serie is NOT stationary.\")<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-335009e elementor-widget elementor-widget-text-editor\" data-id=\"335009e\" 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;\">Et le test en question :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7ee7b26 elementor-widget elementor-widget-code-highlight\" data-id=\"7ee7b26\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>for name, column in df_var_transformed.iteritems():\r\n    dickey_fuller_test(column, name=column.name)\r\n    print('\\n')<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f489b5d elementor-widget elementor-widget-text-editor\" data-id=\"f489b5d\" 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;\">Malheureusement, des s\u00e9ries ne sont pas stationnaires. On va donc diff\u00e9rencier la s\u00e9rie, et r\u00e9it\u00e9rer le test :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-81f0d4c elementor-widget elementor-widget-code-highlight\" data-id=\"81f0d4c\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_diff_1_transformed = df_var_transformed.diff().dropna()\r\nexog_pour_var = exog_pour_var[1:] #we need to offset of 1 because we dropped the first value by differencing\r\nfor name, column in df_diff_1_transformed.iteritems():\r\n    dickey_fuller_test(column, name=column.name)\r\n    print('\\n')<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e50a54e elementor-widget elementor-widget-text-editor\" data-id=\"e50a54e\" 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;\">Maintenant, tout est stationnaire ! On peut passer \u00e0 l&rsquo;entra\u00eenement du mod\u00e8le.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-683ad01 elementor-widget elementor-widget-menu-anchor\" data-id=\"683ad01\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"modele\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9b7fad9 e-flex e-con-boxed e-con\" data-id=\"9b7fad9\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-951e381 elementor-widget elementor-widget-heading\" data-id=\"951e381\" 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\">5. Le mod\u00e8le et la convergence lag\/variables<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b50bb81 elementor-widget elementor-widget-menu-anchor\" data-id=\"b50bb81\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"Selectionner_des_variables\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f00e3e elementor-widget elementor-widget-heading\" data-id=\"0f00e3e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">a. S\u00e9lectionner des variables<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c95d580 elementor-widget elementor-widget-text-editor\" data-id=\"c95d580\" 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;\">Lorsque l\u2019on r\u00e9alise un mod\u00e8le de classification ou de r\u00e9gression plus \u201cclassique\u201d, on teste toujours la pertinence des variables en input, c\u2019est-\u00e0-dire la qualit\u00e9 de l\u2019information d\u00e9livr\u00e9e par ces variables pour pr\u00e9dire la variable cible. Dans un exercice de s\u00e9ries temporelles, c\u2019est la m\u00eame chose : il se peut qu\u2019une variable n\u2019explique pas\/trop peu la variable cible. Il faut donc d\u00e9terminer lesquelles garder, lesquelles supprimer. \ud83e\udd17<\/span><\/p><p><span style=\"font-weight: 400;\">Dans notre cas, il existe un test, le test de Granger, qui permet de terminer si une variable permet d\u2019expliquer les pr\u00e9dictions d\u2019une autre variable. C\u2019est exactement ce que l\u2019on cherche \ud83d\ude00\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Voici la fonction du test :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f7e96d5 elementor-widget elementor-widget-code-highlight\" data-id=\"f7e96d5\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def grangers_test(data, lag, test='ssr_chi2test',verbose=False):    \r\n    \"\"\"_summary_\r\n        The values inside the dataframe are the p-value of the test for the couple feature X\/Y\r\n    H0 hypothesis is the following :\r\n        \"Forecasts of X does not influence forecasts on Y\"\r\n    Therefor, p-value under 0.005 threshold allows us to reject H0 with a confidence level of 95% and pushs us to keep this couple of variables\r\n\r\n\r\nLes arguments sont :\r\n        data (dataframe): dataframe that holds the value of each feature\r\n        lag (int): the lag to apply to the test. Must be equal to the lag used in the model\r\n        test (str, optional): the test to apply. Defaults to 'ssr_chi2test'.\r\n        verbose (bool, optional):  Defaults to False.\r\n\r\n\r\n    Returns:\r\n        the dataframe with p-value\r\n    \"\"\"\r\n    df = pd.DataFrame(np.zeros((len(data.columns), len(data.columns))), columns=data.columns, index=data.columns)\r\n    for col in df.columns:\r\n        for row in df.index:\r\n            test_result = grangercausalitytests(data[[row, col]], maxlag=[lag], verbose=False)\r\n            p_values = round(test_result[lag][0][test][1],4) #on va avoir toutes les p-valeurs une part lag\r\n            p_value = np.min(p_values) #On s'int\u00e9resse \u00e0 la valeur minimale des p-valeur\r\n            df.loc[row, col] = p_value\r\n    df.columns = [var for var in data.columns]\r\n    df.index = [var + '_Y' for var in data.columns]\r\n    return df<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1454715 elementor-widget elementor-widget-text-editor\" data-id=\"1454715\" 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 plus de la fonction qui teste, on met en place une fonction qui va r\u00e9duire notre dataset initial, en fonction des r\u00e9sultats du test : on teste le dataframe, on supprime la variable avec la somme des p-value la plus forte, et on it\u00e8re jusqu\u2019\u00e0 ce que toutes les variables passent le test. <\/span><\/p><p><span style=\"font-weight: 400;\">\u00c0 noter que l\u2019on peut rentrer une \u00ab\u00a0targeted feature\u00a0\u00bb qui nous permet de ne jamais supprimer une variable en particulier que l\u2019on voudrait cibler. En valeur retour, la fonction renvoie le dataframe r\u00e9duit en dimentionalit\u00e9. Il ne reste que des variables dont les pr\u00e9dictions contribuent \u00e0 pr\u00e9dire chacune des autre variables :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4cd13a7 elementor-widget elementor-widget-code-highlight\" data-id=\"4cd13a7\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def reduce_dim_granger_test(df_to_reduce, lag_to_apply, targeted_feature = None):\r\n    \"\"\"We reduce the dataset thanks to the granger test\r\n        We test that every variables in the dataframe are usefull to predict each other, and if not, we drop them\r\n        After each iteration of \"features optimization\", we run again the model fit in order to verify that the best lag_order has not changed.\r\n        If it as, hwe run the granger test optimization again\r\n    Args:\r\n        df_to_reduce (dataframe to reduce): the data frame we want to reduce\r\n        lag_to_apply (int): the current lag order of the model we use in that precise iteration\r\n        targeted_feature(string)\r\n\r\n\r\n    Returns:\r\n        _type_: we return the dataframe that has been reduced\r\n    \"\"\"\r\n    df_granger = grangers_test(df_to_reduce, lag = lag_to_apply)\r\n    np.fill_diagonal(df_granger.values, 0)\r\n    #plt.figure(figsize = (16,5))\r\n    #sns.heatmap(df_granger, annot = True)\r\n    #plt.show()\r\n    while (df_granger.values>= 0.05).any():\r\n        list_feature_non_granger_causal = []\r\n        list_value_non_granger_causal = []\r\n        for col in df_granger.columns:\r\n            if (df_granger[col].values >= 0.05).any() and col != targeted_feature:\r\n                list_feature_non_granger_causal.append(col)\r\n                list_value_non_granger_causal.append(sum(df_granger[col].values))\r\n        df_feature_to_pop = pd.DataFrame(list_value_non_granger_causal, index = list_feature_non_granger_causal, columns=['p-value'])  \r\n        df_to_reduce = df_to_reduce.drop(df_feature_to_pop['p-value'].idxmax(), axis = 1)\r\n        df_granger = grangers_test(df_to_reduce, lag = 5)\r\n        np.fill_diagonal(df_granger.values, 0)\r\n        #plt.figure(figsize = (16,5))\r\n        #sns.heatmap(df_granger, annot = True)\r\n\r\n\r\n    return df_to_reduce<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d0b6e2b elementor-widget elementor-widget-text-editor\" data-id=\"d0b6e2b\" 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;\">On peut voir que la fonction utilise un param\u00e8tre qui est le \u201clag\u201d : il s\u2019agit du param\u00e8tre de notre mod\u00e8le dont nous parlions plus t\u00f4t. En fonction du lag retenu, le test ne renverra pas les m\u00eames valeurs. Il est donc tr\u00e8s important de sp\u00e9cifier ce lag en fonction du lag du mod\u00e8le\u2026 C\u2019est l\u00e0 que les choses se compliquent un peu.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-17265b9 elementor-widget elementor-widget-menu-anchor\" data-id=\"17265b9\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"Selection_du_lag_optimal\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-056f070 elementor-widget elementor-widget-heading\" data-id=\"056f070\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">b. S\u00e9lection du lag optimal<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ff3bf93 elementor-widget elementor-widget-text-editor\" data-id=\"ff3bf93\" 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;\">On va vouloir trouver la valeur lambda qui minimise l\u2019erreur choisie sur la variable choisie. Pour cela, on peut soit passer par une m\u00e9thode disponible dans le package statsmodels, soit utiliser une fonction maison lorsque les m\u00e9triques de la librairie ne nous conviennent pas. <\/span><\/p><p><span style=\"font-weight: 400;\">En effet, statsmodels ne permet d\u2019optimiser un mod\u00e8le VAR que sur des m\u00e9triques statistiques. Or, il n\u2019est pas forc\u00e9ment bon d\u2019optimiser seulement les m\u00e9triques statistiques (AIC, BIC). Dans notre cas, cherchons plut\u00f4t \u00e0 optimiser la MAE. Pour cela, nous allons devoir, pour chacune des valeurs (<\/span><i><span style=\"font-weight: 400;\">lambda<\/span><\/i><span style=\"font-weight: 400;\">) de l\u2019it\u00e9ration, calculer notre m\u00e9trique cible, ce qui veut donc dire :\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pour un niveau de lag (<\/span><i><span style=\"font-weight: 400;\">lambda)<\/span><\/i><span style=\"font-weight: 400;\"> choisi, on doit tester la pertinences des variables gr\u00e2ce \u00e0 notre test de granger et le cas \u00e9ch\u00e9ant, \u00e9liminer les features inutiles<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Avoir une fonction qui va d\u00e9-transformer notre pr\u00e9diction (pour rappel, on fonctionne actuellement avec des variables qui sont transform\u00e9es via boxcox, minmaxscaler, puis diff\u00e9renci\u00e9es !)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Avoir une fonction de predict<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Avoir des fonctions de mesure de l\u2019erreur<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Garder en m\u00e9moire le meilleur mod\u00e8le \u00e0 date pour la m\u00e9trique choisie, ici la MAE.<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1aa935b elementor-widget elementor-widget-text-editor\" data-id=\"1aa935b\" 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;\">Dans le cadre de cet exemple, mes mod\u00e8les sont test\u00e9s \u00e0 chaque fois sur la variable que j\u2019ai termin\u00e9e comme \u00e9tant ma cible (tsd). Je ne mesure donc pas (et je n\u2019optimise pas) en fonction de la capacit\u00e9 qu\u2019a l\u2019algorithme \u00e0 bien pr\u00e9dire l\u2019ensemble des variables.<\/span><\/p><p><span style=\"font-weight: 400;\">On va avoir besoin d\u2019une fonction predict :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f050bed elementor-widget elementor-widget-code-highlight\" data-id=\"f050bed\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def predict_results(model_fitted, training_set, exog_for_predicting):\r\n    \"\"\"function to predict the forecasts\r\n\r\n\r\n    Args:\r\n        model_fitted (var model): the fitted model\r\n        training_set (dataframe): the training set  \r\n        exog_for_predicting (dataframe): exog on the index of predicting\r\n\r\n\r\n    Returns:\r\n        dataframe : returns three dataframe : the actual predictions, the upper confidence interval, the lower confidence interval\r\n    \"\"\"\r\n    lag_order = model_fitted.k_ar\r\n    input_data = training_set.values[-lag_order:]\r\n    y_predicted = model_fitted.forecast(y = input_data, steps = len(exog_for_predicting), exog_future=exog_for_predicting)\r\n    df_predicted_interval = model_fitted.forecast_interval(y = input_data, steps = len(exog_for_predicting), exog_future=exog_for_predicting)\r\n    interval_upper = pd.DataFrame(df_predicted_interval[2],  index=exog_for_predicting.index, columns=training_set.columns)\r\n    interval_lower = pd.DataFrame(df_predicted_interval[1], index=exog_for_predicting.index, columns=training_set.columns)\r\n\r\n\r\n    df_predicted = pd.DataFrame(y_predicted, index=exog_for_predicting.index, columns=training_set.columns)\r\n    return df_predicted, interval_upper, interval_lower<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4784034 elementor-widget elementor-widget-text-editor\" data-id=\"4784034\" 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;\">Puis de re-transformer les variables, d\u2019abord en inversant la diff\u00e9renciation :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b96f92c elementor-widget elementor-widget-code-highlight\" data-id=\"b96f92c\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def inv_diff(df_orig, df_forecast, second_diff = False):\r\n    \"\"\"invert the differentiation of a dataframe\r\n\r\n\r\n    Args:\r\n        df_orig (dataframe): the dataframe that existed JUST BEFORE differencing\r\n        df_forecast (dataframe): the dataframe with the forecasted values\r\n        second_diff (bool, optional): Did you apply two diff order ?\r\n\r\n\r\n    Returns:\r\n        dataframe with the diff reverted\r\n    \"\"\"\r\n    columns = df_forecast.columns\r\n    df_fc_inv = df_forecast.copy()\r\n    n_jour_cible = len(df_forecast)\r\n    for col in columns:\r\n        if second_diff:\r\n            df_fc_inv[str(col)+'_1d'] = (df_orig[col].iloc[-n_jour_cible-1]-df_orig[col].iloc[-n_jour_cible-2]) + df_fc_inv[str(col)].cumsum()\r\n            df_fc_inv[str(col)] = df_orig[col].iloc[-n_jour_cible-1] + df_fc_inv[str(col)+\"_1d\"].cumsum()\r\n        else:\r\n            df_fc_inv[str(col)] = df_orig[col].iloc[-n_jour_cible-1] + df_fc_inv[str(col)].cumsum()\r\n    return df_fc_inv<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f532d0 elementor-widget elementor-widget-text-editor\" data-id=\"0f532d0\" 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;\">Puis en inversant les transformations de boxcox &amp; minmaxscaler sur les bonnes variables :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7f9cfd5 elementor-widget elementor-widget-code-highlight\" data-id=\"7f9cfd5\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def invert_transform(list_of_features_boxcox, list_of_features_normalized, scaler, predicted, initial_dataframe, dict_lambda_value):\r\n    \"\"\"invert the transformation boxcox and of a scaler of any kind\r\n\r\n\r\n    Args:\r\n        list_of_features_boxcox (list): list of features you transformed with Boxcox\r\n        list_of_features_normalized (list): list of features you normalized\r\n        scaler (scaler objet): the scaler you innitiated for normalizing\r\n        predicted (dataframe): forecasted dataframe\r\n        initial_dataframe (dataframe: the very first dataframe, not transformed\r\n        dict_lambda_value (_type_): the dict  in we stored the lambdas values of each feature transformed via boxcox\r\n\r\n\r\n    Returns:\r\n        the predicted dataframe with true destransformed value\r\n    \"\"\"\r\n    list_of_features_boxcox = list(set(list_of_features_boxcox) & set(predicted.columns))\r\n    list_of_features_normalized = list(set(list_of_features_normalized) & set(predicted.columns))\r\n\r\n\r\n    scaler = scaler.fit(initial_dataframe[list_of_features_boxcox])\r\n    predicted[list_of_features_normalized] = scaler.inverse_transform(predicted[list_of_features_normalized])\r\n    for col in list_of_features_boxcox:\r\n        predicted[col]=inv_boxcox(predicted[col], dict_lambda_value[col]).values\r\n   \r\n    return predicted<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1fd3e0b elementor-widget elementor-widget-text-editor\" data-id=\"1fd3e0b\" 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;\">Et enfin, diff\u00e9rentes fonctions perso qui permettent de mesurer les erreurs :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b7c9583 elementor-widget elementor-widget-code-highlight\" data-id=\"b7c9583\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def r2_ajusted(r2, df):\r\n    longueur = len(df.index)\r\n    nb_col = len(df.columns)\r\n    score_ajusted = 1-((1-r2)*(longueur-1) \/ (longueur - nb_col -1))\r\n    return score_ajusted<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-930090b elementor-widget elementor-widget-code-highlight\" data-id=\"930090b\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def mape(y_test, pred):\r\n    y_test, pred = np.array(y_test), np.array(pred)\r\n    mape = np.mean(np.abs((y_test - pred) \/ y_test))\r\n    return mape<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cce7e67 elementor-widget elementor-widget-text-editor\" data-id=\"cce7e67\" 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;\">Et on a finalement notre fonction d\u2019optimisation, qui enregistre les metrics de chacune des it\u00e9rations : <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eee4471 elementor-widget elementor-widget-code-highlight\" data-id=\"eee4471\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def convergence_lag_features(transformed_diff_dataframe, transformed_dataframe, initial_dataframe, list_of_features_boxcox, list_of_features_normalized, scaler, dict_lambda_value,\r\n                             exog, maxlag_to_converge, n_period, targeted_feature):\r\n    \"\"\"We will optimize the features according to the chosen lag until the lag and features do not change\r\n\r\n\r\n    Args:\r\n        initial_transforemd_diff_dataframe (Dataframe): The initial dataframe you want to perform the convergence on. It is the dataframe you want the data\r\n        to be trained on, so it must be transformed, differenciated if needed...\r\n        transformed_dataframe (Dataframe): The initial dataframe that is transformed but not yet differenciated\r\n        exog (pandas dataframe): the exogeneous features you give to your model. Must be known for train and test ! Good example is holidays,\r\n        Fourier features...\r\n        maxlag_to_converge (int): the maximum number of lags to include in your model. The code will test them all so the bigger the longer\r\n        the training time ! Be careful as it is exponential UwU\r\n        n_period (int): number of time periods (days, hours...) you want to predict\r\n        targeted_feature: the main feature you want to predict\r\n\r\n\r\n    Returns:\r\n    best_model (model object) : the best fitted model among all p\r\n    training_set (pandas dataframe) : the training set being granger tested and reduced\r\n    training_set_exog (pandas dataframe) : the training set exog\r\n    testing_set (pandas dataframe) : the test set being granger tested and reduced\r\n    test_set_exog (pandas dataframe) : the testing set exog\r\n    transformed_dataframe_updated (pandas dataframe) :\r\n    training_metrics\r\n    initial_dataframe_uptaded\r\n    \"\"\"\r\n    mae_training_loop = []\r\n    MAPE_training_loop = []\r\n    aic_training_loop = []\r\n    r2_training_loop= []\r\n    normality_training_loop = []\r\n    whiteness_training_loop = []\r\n    best_model = None\r\n    best_df_diff = None\r\n\r\n\r\n    training_set_exog = exog[:-n_period]\r\n    test_set_exog = exog[-n_period:]\r\n    initial_testing_set = initial_dataframe[-n_period:]\r\n\r\n\r\n    for i in range(1, maxlag_to_converge):\r\n        df_diff = transformed_diff_dataframe.copy()\r\n        df_diff= reduce_dim_granger_test(df_diff, i, targeted_feature)\r\n\r\n\r\n        training_set=df_diff[:-n_period]\r\n        testing_set = df_diff[-n_period:]\r\n\r\n\r\n        model = VAR(endog = training_set, exog = training_set_exog)\r\n        model = model.fit(i)\r\n\r\n\r\n        predict, predict_upper, predict_lower = predict_results(model, training_set, test_set_exog)\r\n\r\n\r\n        initial_testing_set_updated = initial_testing_set[predict.columns]\r\n        initial_dataframe_uptaded = initial_dataframe[predict.columns]\r\n       \r\n        predict = inv_diff(transformed_dataframe, predict)\r\n        predict = invert_transform(list_of_features_boxcox, list_of_features_normalized, scaler, predict, initial_dataframe, dict_lambda_value)\r\n\r\n\r\n        mae = mean_absolute_error(initial_testing_set_updated[targeted_feature], predict[targeted_feature])\r\n        if len(mae_training_loop) == 0 or min(mae_training_loop) > mae:\r\n            best_model = model\r\n            best_df_diff = df_diff\r\n        mae_training_loop.append(mae)\r\n        MAPE_training_loop.append(mape(initial_testing_set_updated[targeted_feature], predict[targeted_feature]))\r\n        r2_training_loop.append(r2_ajusted(r2_score(initial_testing_set_updated[targeted_feature], predict[targeted_feature]), predict))\r\n        aic_training_loop.append(model.aic)\r\n        normality_training_loop.append(model.test_normality().pvalue)\r\n        whiteness_training_loop.append(model.test_whiteness(round((len(training_set))\/5)).pvalue)\r\n\r\n\r\n   \r\n    training_metrics = pd.DataFrame()\r\n    training_metrics['mae'] = mae_training_loop\r\n    training_metrics['mape'] = MAPE_training_loop\r\n    training_metrics['r2'] = r2_training_loop\r\n    training_metrics['aic'] = aic_training_loop\r\n    training_metrics['normality'] = normality_training_loop  #H0: distribution is gaussian. if pvalue < 0.05 we reject and that is not good\r\n    training_metrics['whiteness'] =  whiteness_training_loop   #H0: there is no presence of autocorrelation. if pvalue < 0.05 we reject and that is not good\r\n\r\n\r\n    training_set=best_df_diff[:-n_period]\r\n    testing_set = best_df_diff[-n_period:]\r\n    initial_dataframe_uptaded = initial_dataframe[best_df_diff.columns]\r\n    transformed_dataframe_updated = transformed_dataframe[best_df_diff.columns]\r\n    return best_model, training_set, training_set_exog, testing_set, test_set_exog, transformed_dataframe_updated, training_metrics, initial_dataframe_uptaded<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9911b76 elementor-widget elementor-widget-text-editor\" data-id=\"9911b76\" 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;\">On appelle le code en choisissant notre lag maximum \u00e0 tester, ici 52 :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a11569 elementor-widget elementor-widget-code-highlight\" data-id=\"6a11569\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>model_var, train_var, train_var_exog, test_var, test_var_exog, df_var_transformed, df_optimizing_metrics, df_var = convergence_lag_features(df_diff_1_transformed, df_var_transformed, df_var, list_features_to_box_cox, list_features_non_box_cox,\r\n                                                                                                                                      minmaxscaler, dict_lambda_bc, exog_pour_var, 52, n_period_predict, target_variable)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-02efa26 elementor-widget elementor-widget-text-editor\" data-id=\"02efa26\" 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;\">On trouve un compte rendu de toutes les it\u00e9rations dans le dataframe \u00ab\u00a0df_optimizing_metrics\u00a0\u00bb.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ab5ffad elementor-widget elementor-widget-menu-anchor\" data-id=\"ab5ffad\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"prediction\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3cdfc2d e-flex e-con-boxed e-con\" data-id=\"3cdfc2d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-89ce6e0 elementor-widget elementor-widget-heading\" data-id=\"89ce6e0\" 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\">6. Pr\u00e9diction avec le meilleur mod\u00e8le et affichage des r\u00e9sultats<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4aa8dc2 elementor-widget elementor-widget-text-editor\" data-id=\"4aa8dc2\" 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;\">Maintenant que l\u2019on a notre meilleur mod\u00e8le optimis\u00e9 avec les training\/testing set aussi optimis\u00e9s en termes de choix de variables, avec aussi le dataframe initial avec les variables s\u00e9lectionn\u00e9s, on peut pr\u00e9dire, inverser les transformations (je pr\u00e9dis en m\u00eame temps les intervals de confiance, et je les d\u00e9-transforme aussi) :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d1b1a5f elementor-widget elementor-widget-code-highlight\" data-id=\"d1b1a5f\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_predicted, df_interval_lower, df_interval_upper = predict_results(model_var, train_var, test_var_exog)\r\n\r\n\r\ndf_predicted = inv_diff(df_var_transformed, df_predicted)\r\ndf_interval_lower = inv_diff(df_var_transformed, df_interval_lower)\r\ndf_interval_upper = inv_diff(df_var_transformed,df_interval_upper)\r\ndf_predicted = invert_transform(list_features_to_box_cox, list_features_non_box_cox, minmaxscaler,\r\n                                df_predicted, df_var, dict_lambda_bc)\r\ndf_interval_lower = invert_transform(list_features_to_box_cox, list_features_non_box_cox, minmaxscaler,\r\n                                df_interval_lower, df_var, dict_lambda_bc)\r\ndf_interval_upper = invert_transform(list_features_to_box_cox, list_features_non_box_cox, minmaxscaler,\r\n                                df_interval_upper, df_var, dict_lambda_bc)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-af6dff2 elementor-widget elementor-widget-text-editor\" data-id=\"af6dff2\" 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;\">Enfin, je trace mes graphiques true vs pred :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc666b1 elementor-widget elementor-widget-code-highlight\" data-id=\"fc666b1\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>def append_axes(fig, as_cols=False):\r\n    \"\"\"Append new Axes to Figure.\"\"\"\r\n    n = len(fig.axes) + 1\r\n    nrows, ncols = (1, n) if as_cols else (n, 1)\r\n    gs = mpl.gridspec.GridSpec(nrows, ncols, figure=fig)\r\n    for i,ax in enumerate(fig.axes):\r\n        ax.set_subplotspec(mpl.gridspec.SubplotSpec(gs, i))\r\n    return fig.add_subplot(nrows, ncols, n)\r\n\r\n\r\ndef plot_pred_vs_true(true_value, predicted, lower_int, upper_int, normality_of_residual = False):\r\n    \"\"\"_summary_\r\n    The function will plot every true column of the dataframe against pred\r\n\r\n\r\n    Args:\r\n        true_value (dataframe): df containing the true value\r\n        predicted (dataframe): df of the predictions\r\n        lower_int (dataframe) : df with the lower interval values\r\n        upper_int (dataframe) : df with the upper interval values\r\n        normality_of_residuals : are the residuals following a gaussian ? if not, interval will be strange \/EVIL LAUGHTER\/\r\n    \"\"\"\r\n    sns.set(style=\"ticks\", context=\"talk\")\r\n    plt.style.use(\"dark_background\")\r\n    plt.rc('legend',**{'fontsize':25})\r\n    fig = plt.figure(layout='constrained', figsize=(40,70))\r\n    col = predicted.columns\r\n    predicted.columns = predicted.columns+'_pred'\r\n    lower_int.columns =lower_int.columns+'_low_int'\r\n    upper_int.columns = upper_int.columns+'_up_int'\r\n    predicted.plot(subplots=True, ax=append_axes(fig), color='r', fontsize=30, legend=True)\r\n\r\n\r\n    if normality_of_residual:\r\n        lower_int.plot(subplots=True, ax=fig.axes, color='r', fontsize=30, legend=True, linestyle ='-.')\r\n        upper_int.plot(subplots=True, ax=fig.axes, color='r', fontsize=30, legend=True, linestyle ='-.')\r\n    true_value[col].plot(subplots=True, ax=fig.axes, color='b', fontsize=30, legend=True)\r\n    plt.show()<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7bd8900 elementor-widget elementor-widget-code-highlight\" data-id=\"7bd8900\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>plot_pred_vs_true(initial_testing_set, df_predicted, df_interval_lower, df_interval_lower, normality_of_residual=False)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3e74781 elementor-widget elementor-widget-menu-anchor\" data-id=\"3e74781\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"Conclusion\" class=\"elementor-menu-anchor\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4e2955d e-flex e-con-boxed e-con\" data-id=\"4e2955d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4c96115 elementor-widget elementor-widget-heading\" data-id=\"4c96115\" 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\">7. Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7969e46 elementor-widget elementor-widget-text-editor\" data-id=\"7969e46\" 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;\">Dans cet exercice, on atteint une MAE de 3068, une MAPE de 9,4% sur notre variable cible \ud83c\udf89. Voici le graphique true\/pred de la variable cible \u2018tsd\u2019 :\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Si mes r\u00e9sidus ne passent pas le test de normalit\u00e9 (les r\u00e9sidus suivent-ils une gaussienne?) alors je risque de me retrouver avec des intervalles de confiance compl\u00e8tement faux ! Il ne faut donc surtout pas compter dessus. Il existe des m\u00e9thodes pour rendre les r\u00e9sidus gaussiens, mais cela sera le sujet d\u2019un prochain article \ud83d\ude00<\/span><\/p><p><span style=\"font-weight: 400;\">On peut aussi noter qu\u2019en termes d\u2019\u00e9l\u00e9gance de code, on pourrait faire bien mieux avec du code orient\u00e9 objet et en cr\u00e9ant une nouvelle classe qui s&rsquo;appuierait sur le mod\u00e8le VAR de statsmodels.<\/span><\/p><p><span style=\"font-weight: 400;\">Pour conclure, voici le code ex\u00e9cut\u00e9 de A \u00e0 Z en dehors des fonctions :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-efd12eb elementor-widget elementor-widget-code-highlight\" data-id=\"efd12eb\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard \">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df = pd.read_csv(\"path.csv\")\r\ndf['settlement_date'] = pd.to_datetime(df['settlement_date'])\r\ndf = df.set_index('settlement_date')\r\ndf = df.drop(['settlement_period', 'period_hour'], axis = 1)\r\nexog = df[['is_holiday']].copy()\r\ndf = df.drop(['is_holiday'], axis =1)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5a66b46 elementor-widget elementor-widget-code-highlight\" data-id=\"5a66b46\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>target_variable = \"tsd\" #the feature we ultimately want to predict\r\nn_period_predict = 48 * 7 #the number of period we want to predict. I want to predict 7 days and there are 48 data points per day<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e3243a elementor-widget elementor-widget-code-highlight\" data-id=\"1e3243a\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>mask = (df.index > '2022-01-01') #I will use the data post 2022\r\ndf_var = df.loc[mask]\r\nexog_pour_var = exog.loc[mask]\r\ndf_var = df_var +1 #We erase the every value that are equals to 0 in order to facilitate the boxcox transformation<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f7c41e elementor-widget elementor-widget-code-highlight\" data-id=\"1f7c41e\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>initial_testing_set = df_var[-n_period_predict:] #there will be a lot of transformation so we want to keep a safe testing set<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4836272 elementor-widget elementor-widget-code-highlight\" data-id=\"4836272\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>list_features_to_box_cox, list_features_non_box_cox = box_cox_test(df_var)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f79aceb elementor-widget elementor-widget-code-highlight\" data-id=\"f79aceb\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_var_transformed, dict_lambda_bc = transfo_boxcox(df_var, list_features_to_box_cox)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0df1f4f elementor-widget elementor-widget-code-highlight\" data-id=\"0df1f4f\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>#We apply a minmaxscaler transform to the data we could not transform thanks to boxcox\r\nminmaxscaler = MinMaxScaler()\r\nminmaxscaler = minmaxscaler.fit(df_var[list_features_non_box_cox])\r\ndf_var_transformed[list_features_non_box_cox] = minmaxscaler.transform(df_var[list_features_non_box_cox])<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d15fdd5 elementor-widget elementor-widget-code-highlight\" data-id=\"d15fdd5\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>for name, column in df_var_transformed.iteritems():\r\n    dickey_fuller_test(column, name=column.name)\r\n    print('\\n')<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfe5422 elementor-widget elementor-widget-code-highlight\" data-id=\"cfe5422\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_diff_1_transformed = df_var_transformed.diff().dropna()\r\nexog_pour_var = exog_pour_var[1:] #we need to offset of 1 because we dropped the first value by differencing\r\nfor name, column in df_diff_1_transformed.iteritems():\r\n    dickey_fuller_test(column, name=column.name)\r\n    print('\\n')<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-17cc5a2 elementor-widget elementor-widget-code-highlight\" data-id=\"17cc5a2\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>model_var, train_var, train_var_exog, test_var, test_var_exog, df_var_transformed, df_optimizing_metrics, df_var = convergence_lag_features(df_diff_1_transformed, df_var_transformed, df_var, list_features_to_box_cox, list_features_non_box_cox,\r\n                                                                                                                                      minmaxscaler, dict_lambda_bc, exog_pour_var, 52, n_period_predict, target_variable)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-deb3fe5 elementor-widget elementor-widget-code-highlight\" data-id=\"deb3fe5\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>print(df_optimizing_metrics.describe())<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5740b0e elementor-widget elementor-widget-code-highlight\" data-id=\"5740b0e\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>df_predicted, df_interval_lower, df_interval_upper = predict_results(model_var, train_var, test_var_exog)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8260714 elementor-widget elementor-widget-code-highlight\" data-id=\"8260714\" data-element_type=\"widget\" data-widget_type=\"code-highlight.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"prismjs-tomorrow copy-to-clipboard word-wrap\">\n\t\t\t<pre data-line=\"\" class=\"highlight-height language-javascript \">\n\t\t\t\t<code readonly=\"true\" class=\"language-javascript\">\n\t\t\t\t\t<xmp>plot_pred_vs_true(initial_testing_set, df_predicted, df_interval_lower, df_interval_lower, normality_of_residual=False)<\/xmp>\n\t\t\t\t<\/code>\n\t\t\t<\/pre>\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\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Introduction D\u00e9finition du mod\u00e8le VAR : \u00e9quation &amp; int\u00e9r\u00eat Import des libraires, set-up La stationnarit\u00e9 : kezako et pourquoi c\u2019est important Le mod\u00e8le et la convergence lag\/variables a. S\u00e9lectionner des variables b. S\u00e9lection du lag optimal Pr\u00e9diction avec le meilleur mod\u00e8le et affichage des r\u00e9sultats Conclusion 1. Introduction Bienvenue sur cet article explicatif du mod\u00e8le [&hellip;]<\/p>\n","protected":false},"author":78,"featured_media":147086,"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>Le mod\u00e8le VAR : de l\u2019approche m\u00e9tier au plotting des r\u00e9sultats<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez comment d\u00e9velopper une pipeline pour l\u2019ex\u00e9cution d\u2019un mod\u00e8le VAR sous Python, de l\u2019int\u00e9gration de la data jusqu\u2019au plotting des r\u00e9sultats.\" \/>\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\/le-modele-var\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le mod\u00e8le VAR : de l\u2019approche m\u00e9tier au plotting des r\u00e9sultats\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/le-modele-var\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-18T07:30:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T13:43:10+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/03\/illu_VAR_model_blog_4-95.png\" \/>\n\t<meta property=\"og:image:width\" content=\"2560\" \/>\n\t<meta property=\"og:image:height\" content=\"1405\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"J\u00e9r\u00e9my Robert\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"J\u00e9r\u00e9my Robert\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/le-modele-var\",\"url\":\"https:\/\/datascientest.com\/le-modele-var\",\"name\":\"Le mod\u00e8le VAR : de l\u2019approche m\u00e9tier au plotting des r\u00e9sultats\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2023-09-18T07:30:00+00:00\",\"dateModified\":\"2023-11-09T13:43:10+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/7af2361c48e24e79a8aa2360e6e74925\"},\"description\":\"D\u00e9couvrez comment d\u00e9velopper une pipeline pour l\u2019ex\u00e9cution d\u2019un mod\u00e8le VAR sous Python, de l\u2019int\u00e9gration de la data jusqu\u2019au plotting des r\u00e9sultats.\",\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/le-modele-var\"]}]},{\"@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\/7af2361c48e24e79a8aa2360e6e74925\",\"name\":\"J\u00e9r\u00e9my Robert\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/jeremyrobert.jpeg\",\"contentUrl\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/jeremyrobert.jpeg\",\"caption\":\"J\u00e9r\u00e9my Robert\"},\"description\":\"J\u00e9r\u00e9my Robert est actuellement Directeur p\u00e9dagogique B2B chez DataScientest.com. 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