{"id":20971,"date":"2024-02-24T19:20:40","date_gmt":"2024-02-24T18:20:40","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=20971"},"modified":"2024-02-24T19:43:29","modified_gmt":"2024-02-24T18:43:29","slug":"erreurs-de-forecasting","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/","title":{"rendered":"Forecasting errors"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"20971\" class=\"elementor elementor-20971\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-60e73e0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"60e73e0\" data-element_type=\"section\" data-e-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-33 elementor-top-column elementor-element elementor-element-3345ded\" data-id=\"3345ded\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4a20e22 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4a20e22\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Forecasting<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ed3cf05\" data-id=\"ed3cf05\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-09366c2 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"09366c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-764067a\" data-id=\"764067a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e524d13 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"e524d13\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/plat.ai\/blog\/difference-between-prediction-and-forecast\/\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-333fa6b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"333fa6b\" data-element_type=\"section\" data-e-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-0ca2756\" data-id=\"0ca2756\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-56d7d0b elementor-widget elementor-widget-heading\" data-id=\"56d7d0b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/#Erreurs-de-Forecasting\" >Forecasting Errors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/#Mesures-dependants-de-lechelle\" >Scale-dependent measurements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/#Mesures-en-pourcentage\" >Percentage measurements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/#Theil-U-Statistique\" >Theil U Statistics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/forecasting-errors\/#Mesures-relatives\" >Relative measurements<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Erreurs-de-Forecasting\"><\/span>Forecasting Errors<span class=\"ez-toc-section-end\"><\/span><\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-367f2ff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"367f2ff\" data-element_type=\"section\" data-e-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-b3aee43\" data-id=\"b3aee43\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fb80a35 elementor-widget elementor-widget-text-editor\" data-id=\"fb80a35\" data-element_type=\"widget\" data-e-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\t\t<p>Here are the main metrics for measuring forecasting errors:<\/p><p>Scale-dependent measurement:<\/p><ul><li>MAE, MDAE, MSE, RMSE<\/li><\/ul><p>Percentage :<\/p><ul><li>MAPE, sMAPE, MASE, sMdAPE<\/li><\/ul><p>In relative terms:<\/p><ul><li>MRAE, MdRAE, RelMAE<\/li><li>U-statistic<\/li><\/ul><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"forecasting errors\" width=\"97\" height=\"97\" title=\"\"><\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-57b96a9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"57b96a9\" data-element_type=\"section\" data-e-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-3b55a11\" data-id=\"3b55a11\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-27605b0 elementor-widget elementor-widget-heading\" data-id=\"27605b0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Mesures-dependants-de-lechelle\"><\/span>Scale-dependent measurements<span class=\"ez-toc-section-end\"><\/span><\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c90a367 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c90a367\" data-element_type=\"section\" data-e-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-e7299ff\" data-id=\"e7299ff\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0f03013 elementor-widget elementor-widget-text-editor\" data-id=\"0f03013\" data-element_type=\"widget\" data-e-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\t\t<p>We use the following terminology: if y1, \u2026, yn represents a time series, then \u0177i represents the ith predicted value, where i \u2264 n. For i \u2264 n, the ith error ei (aka residual) is then<\/p><p><img decoding=\"async\" class=\"alignnone size-full wp-image-20973\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur1.png\" alt=\"forecasting errors\" width=\"76\" height=\"21\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur1.png 76w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur1-18x5.png 18w\" sizes=\"(max-width: 76px) 100vw, 76px\" \/><\/p><p>Our goal is to find a forecast that minimizes errors. A number of measurements are commonly used to determine the accuracy of a forecast. These include Mean Absolute Error (MAE), Mean Square Error (MSE), and Root Mean Square Error (RMSE).<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-20974 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur2.png\" alt=\"MAE MSE RMSE\" width=\"423\" height=\"53\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur2.png 423w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur2-300x38.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur2-18x2.png 18w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p><p>MdAE calculates the median absolute difference between two digital vectors.<\/p><p>real &lt;- c(1.1, 1.9, 3.0, 4.4, 5.0, 5.6)<br \/>predicted &lt;- c(0.9, 1.8, 2.5, 4.5, 5.0, 6.2)<br \/>mdae (actual, planned)<\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fe6c8c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fe6c8c0\" data-element_type=\"section\" data-e-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-15c777c\" data-id=\"15c777c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9187844 elementor-widget elementor-widget-heading\" data-id=\"9187844\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Mesures-en-pourcentage\"><\/span>Percentage measurements<span class=\"ez-toc-section-end\"><\/span><\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-28ad0ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28ad0ad\" data-element_type=\"section\" data-e-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-6bcaa51\" data-id=\"6bcaa51\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dc66397 elementor-widget elementor-widget-text-editor\" data-id=\"dc66397\" data-element_type=\"widget\" data-e-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\t\t<p>Some other metrics are Mean Absolute Percentage Error (MAPE), Mean Absolute Scale Error (MASE), and Symmetric Mean Absolute Percentage Error (SMAPE).<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20976 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur3.png\" alt=\"MAPE SMAPE MASE\" width=\"592\" height=\"64\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur3.png 592w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur3-300x32.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur3-18x2.png 18w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p><p>Median absolute scale error (MdASE). Taking the median instead of the mean of the absolute testing and training errors makes this metric more robust to outliers since the median tends to be a more robust measure of central tendency in the presence of outliers.<\/p><p>Like MASE and other scaled performance measures, this scale-free measure can be used to compare forecasting methods within a single series or between series.<\/p><p>Just like MASE, this metric is well suited for series with intermittent demand because it will not give infinite or indefinite values unless the training data is a flat time series. In this case the function returns a large value instead of inf.<\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9577065 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9577065\" data-element_type=\"section\" data-e-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-8f38de2\" data-id=\"8f38de2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-23e239e elementor-widget elementor-widget-heading\" data-id=\"23e239e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Theil-U-Statistique\"><\/span>Theil U Statistics<span class=\"ez-toc-section-end\"><\/span><\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-50dd412 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"50dd412\" data-element_type=\"section\" data-e-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-87e32a6\" data-id=\"87e32a6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2074dad elementor-widget elementor-widget-text-editor\" data-id=\"2074dad\" data-element_type=\"widget\" data-e-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\t\t<p>Finally, there is Theil&#039;s U statistic, which is calculated by the formula<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-20977\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur4.png\" alt=\"theil U statistic\" width=\"186\" height=\"57\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur4.png 186w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur4-18x6.png 18w\" sizes=\"(max-width: 186px) 100vw, 186px\" \/><\/p><p>If U &lt; 1, the forecasting technique is better than guessing. If U = 1, then the forecasting technique is equivalent to an estimate. If U &gt; 1, then the forecasting technique is worse than guessing.<\/p><p>In fact, U is also called Theil&#039;s U2 statistic. There is also a less often used U1 stat<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-20978\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur5.png\" alt=\"theil U statistic\" width=\"146\" height=\"57\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur5.png 146w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur5-18x7.png 18w\" sizes=\"(max-width: 146px) 100vw, 146px\" \/><\/p><p>U1 takes values between 0 and 1, with values closer to 0 representing greater forecast accuracy.<\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fb1e388 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fb1e388\" data-element_type=\"section\" data-e-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-5d10f18\" data-id=\"5d10f18\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-66853d5 elementor-widget elementor-widget-heading\" data-id=\"66853d5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Mesures-relatives\"><\/span>Relative measurements<span class=\"ez-toc-section-end\"><\/span><\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-421456e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"421456e\" data-element_type=\"section\" data-e-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-ba113f5\" data-id=\"ba113f5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0265fff elementor-widget elementor-widget-text-editor\" data-id=\"0265fff\" data-element_type=\"widget\" data-e-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\t\t<p>And here are the relative measurements:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-20979\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur6-300x124.png\" alt=\"RE MRAE RELMAE\" width=\"300\" height=\"124\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur6-300x124.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur6-18x7.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/erreur6.png 500w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Here the prediction is to be compared to the so-called reference prediction B.<\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Forecasting Homepage Wiki Forecasting Errors Here are the main metrics to measure forecasting errors: Scale-dependent measurement: MAE, MDAE, \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":20753,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-20971","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/20971","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=20971"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/20971\/revisions"}],"predecessor-version":[{"id":20982,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/20971\/revisions\/20982"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/20753"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=20971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}