{"id":21020,"date":"2024-02-24T20:49:22","date_gmt":"2024-02-24T19:49:22","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=21020"},"modified":"2024-02-24T20:55:39","modified_gmt":"2024-02-24T19:55:39","slug":"pesaran-timmermann","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/prediction-forecast\/pesaran-timmermann\/","title":{"rendered":"Pesaran-Timmermann test"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"21020\" class=\"elementor elementor-21020\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aa4f15e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aa4f15e\" 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 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elementor-col-33 elementor-top-column elementor-element elementor-element-f344b77\" data-id=\"f344b77\" 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-56f17eb elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56f17eb\" 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-e02fec9\" data-id=\"e02fec9\" 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-7f401a3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7f401a3\" 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-668425c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"668425c\" 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-cd2f20a\" data-id=\"cd2f20a\" 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-3cce94f elementor-widget elementor-widget-heading\" data-id=\"3cce94f\" 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\/pesaran-timmermann\/#Test-de-Pesaran-Timmermann\" >Pesaran-Timmermann test<\/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\/pesaran-timmermann\/#Description\" >Description<\/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\/pesaran-timmermann\/#Exemple\" >Example<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Test-de-Pesaran-Timmermann\"><\/span>Pesaran-Timmermann test<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-3a634f3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3a634f3\" 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-0fd72f5\" data-id=\"0fd72f5\" 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-d6110da elementor-widget elementor-widget-text-editor\" data-id=\"d6110da\" 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>The Pesaran-Timmermann test determines whether a forecast correctly predicts the change in direction of a time series. That is to say its directional precision.<\/p><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=\"Pesaran-Timmermann\" 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-2eab9a2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2eab9a2\" 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-9f0dec4\" data-id=\"9f0dec4\" 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-6be2db4 elementor-widget elementor-widget-heading\" data-id=\"6be2db4\" 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=\"Description\"><\/span>Description<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-ecdc8a8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ecdc8a8\" 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-572f8cf\" data-id=\"572f8cf\" 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-b7400de elementor-widget elementor-widget-text-editor\" data-id=\"b7400de\" 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>For any time series ti having n elements, we first define<\/p><p><img decoding=\"async\" class=\"aligncenter size-full wp-image-26016\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image039d.png\" sizes=\"(max-width: 381px) 100vw, 381px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image039d.png 381w, https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image039d-300x40.png 300w\" alt=\"\" width=\"381\" height=\"51\" title=\"\"><\/p><p>Now suppose we have a time series yi with n elements which is predicted by zi and define<\/p><p><img decoding=\"async\" class=\"aligncenter size-full wp-image-26018\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image040d.png\" alt=\"\" width=\"179\" height=\"22\" title=\"\"><\/p><p><a href=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image041d.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26019\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image041d.png\" sizes=\"(max-width: 360px) 100vw, 360px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image041d.png 360w, https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image041d-300x24.png 300w\" alt=\"\" width=\"360\" height=\"29\" title=\"\"><\/a><\/p><p>Under the null hypothesis that z does not predict the direction of change in y (i.e. the sign of yi), we have the following test statistic<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26020\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/01\/image042d.png\" alt=\"PT test statistic\" width=\"146\" height=\"36\" title=\"\"><\/p><p>The Pesaran-Timmermann test is a one-tailed test in which the critical region (where the null hypothesis is rejected) is the upper tail of the standard normal distribution. So if<\/p><p>1 \u2013 NORM.S.DIST(PT, TRUE) &lt; \u03b1<\/p><p>we can then reject the null hypothesis and assert with 1 \u2013 \u03b1 confidence that the forecast accurately predicts the sign of yi.<\/p><p>Note that if the sign of all elements of yi (or zi) is the same, then the PT statistic will not be defined.<\/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-2c56f03 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c56f03\" 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-55c8f9f\" data-id=\"55c8f9f\" 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-dd3071a elementor-widget elementor-widget-heading\" data-id=\"dd3071a\" 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=\"Exemple\"><\/span>Example<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-8146424 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8146424\" 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-0b9f21e\" data-id=\"0b9f21e\" 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-73288f9 elementor-widget elementor-widget-text-editor\" data-id=\"73288f9\" 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>Use the Pesaran-Timmermann test to determine whether the predictions in column B of the figure accurately predict the direction of change for the data in column A.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21026 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/pesaran-timmermann-test1.png\" alt=\"pesaran-timmermann\" width=\"876\" height=\"365\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/pesaran-timmermann-test1.png 876w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/pesaran-timmermann-test1-300x125.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/pesaran-timmermann-test1-768x320.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/pesaran-timmermann-test1-18x8.png 18w\" sizes=\"(max-width: 876px) 100vw, 876px\" \/><\/p><p>The test proves that the forecast accurately predicts the direction of change in the data.<\/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 Home Wiki Pesaran-Timmermann Test The Pesaran-Timmermann test determines whether a forecast correctly predicts the change in direction of a series... <\/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-21020","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/21020","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=21020"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/21020\/revisions"}],"predecessor-version":[{"id":21029,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/21020\/revisions\/21029"}],"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=21020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}