{"id":20986,"date":"2024-02-24T19:45:28","date_gmt":"2024-02-24T18:45:28","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=20986"},"modified":"2024-02-24T20:32:45","modified_gmt":"2024-02-24T19:32:45","slug":"holt-winters","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/pronostico-de-prediccion\/inviernos-altos\/","title":{"rendered":"M\u00e9todo multiplicativo de Holt-Winters"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"20986\" class=\"elementor elementor-20986\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6b2e6b1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6b2e6b1\" 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-d5f03d6\" data-id=\"d5f03d6\" 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-8ccfd39 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8ccfd39\" 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\/es\/pronostico-de-prediccion\/\">\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\">Previsi\u00f3n<\/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 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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-92100eb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"92100eb\" 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-21549ac\" data-id=\"21549ac\" 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-dc2fe35 elementor-widget elementor-widget-heading\" data-id=\"dc2fe35\" 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_87_1 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\">Contenido<\/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=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/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\/es\/pronostico-de-prediccion\/inviernos-altos\/#Methode-multiplicative-de-Holt-Winters\" >M\u00e9todo multiplicativo de Holt-Winters<\/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\/es\/pronostico-de-prediccion\/inviernos-altos\/#Lissage-exponentiel-simple-Exponential-Smoothing\" >Suavizado exponencial simple<\/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\/es\/pronostico-de-prediccion\/inviernos-altos\/#Tendance-lineaire-de-Holt\" >tendencia lineal de Holt<\/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\/es\/pronostico-de-prediccion\/inviernos-altos\/#Methode-de-Holt-Winters-multiplicative\" >M\u00e9todo multiplicativo de Holt-Winters<\/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\/es\/pronostico-de-prediccion\/inviernos-altos\/#Methode-additive-Holt-Winters\" >M\u00e9todo aditivo de Holt-Winters<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Methode-multiplicative-de-Holt-Winters\"><\/span>M\u00e9todo multiplicativo de Holt-Winters<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-a26ea57 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a26ea57\" 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-c50fe34\" data-id=\"c50fe34\" 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-2149831 elementor-widget elementor-widget-text-editor\" data-id=\"2149831\" 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>As\u00ed funciona el m\u00e9todo de suavizado multiplicativo o triple de Holt-Winters.<\/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=\"Holt-Winters\" 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-e3e9ed3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e3e9ed3\" 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-c46eded\" data-id=\"c46eded\" 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-31573e3 elementor-widget elementor-widget-heading\" data-id=\"31573e3\" 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=\"Lissage-exponentiel-simple-Exponential-Smoothing\"><\/span>Suavizado exponencial simple<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-b300c16 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b300c16\" 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-885b061\" data-id=\"885b061\" 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-30b6bd6 elementor-widget elementor-widget-text-editor\" data-id=\"30b6bd6\" 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>En el suavizado exponencial simple (tambi\u00e9n conocido como simple), el valor predicho en el momento i+1 se basa en el valor en el momento i y el valor predicho en el momento i (y, por lo tanto, indirectamente en todos los valores de tiempo anteriores). En particular, para alg\u00fan \u03b1 donde 0 \u2264 \u03b1 \u2264 1, para todo i &gt; 1, definimos<\/p><p><img decoding=\"async\" class=\"alignnone size-full wp-image-20994\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters1.png\" alt=\"inviernos-holt\" width=\"189\" height=\"21\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters1.png 189w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters1-18x2.png 18w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><\/p><p>Tenga en cuenta que no incluimos el tiempo i = 1 en los c\u00e1lculos de MAE y MSE.<\/p><p>En <a href=\"https:\/\/complex-systems-ai.com\/es\/logica-matematica-27\/\">\u00e1lgebra<\/a> simple, esta iteraci\u00f3n tambi\u00e9n se puede expresar como<\/p><p><img decoding=\"async\" class=\"alignnone size-full wp-image-20995\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters2.png\" alt=\"suavizado exponencial\" width=\"239\" height=\"21\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters2.png 239w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters2-18x2.png 18w\" sizes=\"(max-width: 239px) 100vw, 239px\" \/><\/p><p>Veamos la f\u00f3rmula con Excel. La f\u00f3rmula en la celda C4 es =B4 y la f\u00f3rmula en la celda C5 es =C4+B$21*(B4-C4).<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20996 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters3.png\" alt=\"Suavizado exponencial\" width=\"859\" height=\"444\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters3.png 859w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters3-300x155.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters3-768x397.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters3-18x9.png 18w\" sizes=\"(max-width: 859px) 100vw, 859px\" \/><\/p><p>El pron\u00f3stico para el siguiente valor en la serie temporal es 74,0 (celda C19), usando la f\u00f3rmula =C18+B$21*(B18-C18)<\/p><p>Excel proporciona la herramienta de an\u00e1lisis de datos de suavizado exponencial para simplificar los c\u00e1lculos descritos anteriormente.<\/p><p>Para utilizar esta herramienta, por ejemplo, seleccione Datos &gt; An\u00e1lisis|<a href=\"https:\/\/complex-systems-ai.com\/es\/analisis-de-datos\/\">An\u00e1lisis de datos<\/a> y elija Suavizado exponencial en el men\u00fa que aparece. Ahora aparece un cuadro de di\u00e1logo. Se utiliza un campo Factor de amortiguaci\u00f3n en lugar del campo Intervalo. Si este campo se deja en blanco, su valor predeterminado es 0,7.<\/p><p>El factor de amortiguaci\u00f3n es s\u00f3lo 1 \u2013 \u03b1. As\u00ed, por ejemplo, deber\u00eda utilizar 0,6 como factor de amortiguaci\u00f3n.<\/p><p>El resultado se presenta en las columnas D y E de la figura con el gr\u00e1fico.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20998 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters4.png\" alt=\"Suavizado exponencial\" width=\"746\" height=\"364\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters4.png 746w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters4-300x146.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters4-18x9.png 18w\" sizes=\"(max-width: 746px) 100vw, 746px\" \/><\/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-7a619ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7a619ad\" 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-77a5e19\" data-id=\"77a5e19\" 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-eab5aab elementor-widget elementor-widget-heading\" data-id=\"eab5aab\" 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=\"Tendance-lineaire-de-Holt\"><\/span>tendencia lineal de Holt<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-0140827 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0140827\" 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-dd3af9c\" data-id=\"dd3af9c\" 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-9d6c8ff elementor-widget elementor-widget-text-editor\" data-id=\"9d6c8ff\" 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>Los datos de la figura anterior de suavizado exponencial simple (as\u00ed como las cifras anteriores de esta p\u00e1gina web) muestran una clara tendencia al alza. Los m\u00e9todos de media m\u00f3vil y de suavizado exponencial \u00fanico no modelan esto adecuadamente, pero el m\u00e9todo de tendencia lineal de Holt (tambi\u00e9n conocido como suavizado doble exponencial) s\u00ed lo hace. Esto se logra agregando un segundo modelo de suavizado exponencial \u00fanico para capturar la tendencia (al alza o a la baja). El modelo toma la siguiente forma para todo i &gt; 1.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22003 size-full\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image002z.png\" alt=\"Suavizado exponencial doble\" width=\"127\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22004 size-full\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image003z.png\" alt=\"Suavizado exponencial doble\" width=\"209\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22005 size-full\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image004z.png\" alt=\"Suavizado exponencial doble\" width=\"209\" height=\"21\" title=\"\"><\/p><p><a href=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image005z.png\" rel=\"attachment wp-att-22006 nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22006\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image005z.png\" alt=\"imagen005z\" width=\"92\" height=\"21\" title=\"\"><\/a><\/p><p>donde 0 \u2264 \u03b1 \u2264 1 y 0 &lt; \u03b2 \u2264 1.<\/p><p>Una forma alternativa de estas ecuaciones es<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22003\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image002z.png\" alt=\"imagen002z\" width=\"127\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22007\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image006z.png\" alt=\"imagen006z\" width=\"146\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22008\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image007z.png\" alt=\"imagen007z\" width=\"109\" height=\"21\" title=\"\"><\/p><p><a href=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image005z.png\" rel=\"attachment wp-att-22006 nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22006\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image005z.png\" alt=\"imagen005z\" width=\"92\" height=\"21\" title=\"\"><\/a><\/p><p>O<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22009\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image008z.png\" alt=\"imagen008z\" width=\"226\" height=\"21\" title=\"\"><\/p><p>Si beta=0 entonces tenemos una exponenciaci\u00f3n simple.<\/p><p>El resultado se presenta en la figura. Aqu\u00ed, la celda C4 contiene la f\u00f3rmula =B4, la celda D4 contiene el valor 0, la celda C5 contiene la f\u00f3rmula =B$21*B5+(1-B$21)*(C4+D4), la celda D5 contiene la f\u00f3rmula =C$21* (C5-C4 )+(1-C$21)*D4 y la celda E5 contiene la f\u00f3rmula =C4+D4.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21000 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters7.png\" alt=\"Suavizado exponencial doble\" width=\"988\" height=\"448\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters7.png 988w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters7-300x136.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters7-768x348.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters7-18x8.png 18w\" sizes=\"(max-width: 988px) 100vw, 988px\" \/><\/p><p>Para cualquier valor de i, el pron\u00f3stico en el momento i+h viene dado por la f\u00f3rmula<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22010\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image009z.png\" alt=\"imagen009z\" width=\"101\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21001 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters8.png\" alt=\"inviernos-holt\" width=\"732\" height=\"465\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters8.png 732w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters8-300x191.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters8-18x12.png 18w\" sizes=\"(max-width: 732px) 100vw, 732px\" \/><\/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-ca80f83 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ca80f83\" 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-3e45f4f\" data-id=\"3e45f4f\" 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-efd985c elementor-widget elementor-widget-heading\" data-id=\"efd985c\" 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=\"Methode-de-Holt-Winters-multiplicative\"><\/span>M\u00e9todo multiplicativo de Holt-Winters<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-0b0a4f7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0b0a4f7\" 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-99da799\" data-id=\"99da799\" 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-97001d1 elementor-widget elementor-widget-text-editor\" data-id=\"97001d1\" 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>En el m\u00e9todo Holt-Winters (tambi\u00e9n conocido como suavizado triple exponencial), agregamos un componente estacional al modelo de tendencia lineal de Holt. Exploramos dos de estos modelos: el modelo de estacionalidad multiplicativa y el modelo de estacionalidad aditiva. Consideramos el primero de estos modelos en esta p\u00e1gina web. Consulte el modelo aditivo de Holt-Winters para el segundo modelo.<\/p><p>Sea c la duraci\u00f3n de un ciclo estacional. As\u00ed, c = 12 para los meses de un a\u00f1o, c = 7 para los d\u00edas de una semana y c = 4 para los trimestres de un a\u00f1o. El modelo toma la siguiente forma recursiva para todo i &gt; c<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-26562 size-full\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/03\/image159d.png\" alt=\"Ecuaci\u00f3n u de Holt-Winter\" width=\"246\" height=\"20\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-22005\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2016\/03\/image004z.png\" alt=\"imagen004z\" width=\"209\" height=\"21\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-26563 size-full\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2018\/03\/image160d.png\" alt=\"Ecuaci\u00f3n de Holt-Winter\" width=\"171\" height=\"20\" title=\"\"><\/p><p>donde 0 \u2264 \u03b1 \u2264 1, 0 \u2264 \u03b2 \u2264 1 y 0 \u2264 \u03b3 \u2264 1.<\/p><p>Los valores de ui representan la l\u00ednea de base, los valores de vi representan la tendencia (es decir, la pendiente) y los valores de si representan el componente estacional. En el modelo multiplicativo, para cualquier c per\u00edodos de tiempo consecutivos, la suma de los valores de si es aproximadamente igual a c (al menos para valores razonables de \u03b1, \u03b2, \u03b3).<\/p><p>Las predicciones para los elementos de datos yi se pueden expresar como<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-28460\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image005m.png\" alt=\"Valores y previstos\" width=\"143\" height=\"21\" title=\"\"><\/p><p>Para pron\u00f3sticos en tiempos futuros, utilizamos el formulario<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-28461\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image006m.png\" alt=\"Valores futuros previstos\" width=\"165\" height=\"21\" title=\"\"><\/p><p>donde h\u2032 =INT((h\u20131)\/c)+1.<\/p><p>Formas alternativas<br \/>Tambi\u00e9n podemos utilizar la siguiente versi\u00f3n alternativa del t\u00e9rmino estacionalidad:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33936\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image041.png\" sizes=\"(max-width: 258px) 100vw, 258px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2021\/06\/image041.png 334w, https:\/\/real-statistics.com\/wp-content\/uploads\/2021\/06\/image041-300x31.png 300w\" alt=\"T\u00e9rmino de estacionalidad alternativo\" width=\"258\" height=\"27\" title=\"\"><\/p><p>Con base en esta versi\u00f3n del t\u00e9rmino de estacionalidad, tenemos la siguiente forma alternativa de las ecuaciones recursivas:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33937\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image042.png\" alt=\"T\u00e9rmino u_i alternativo\" width=\"207\" height=\"24\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33938\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image043.png\" alt=\"T\u00e9rmino v_i alternativo\" width=\"164\" height=\"24\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33939\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image044.png\" alt=\"T\u00e9rmino alternativo s_i\" width=\"218\" height=\"24\" title=\"\"><\/p><p><a href=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image045.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33940\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image045.png\" alt=\"y_i alternativa\" width=\"201\" height=\"24\" title=\"\"><\/a><\/p><p>Los valores iniciales del modelo, es decir, donde 1 \u2264 i \u2264 c, son<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-28462\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image007m.png\" alt=\"Valores iniciales Holt-Winters\" width=\"255\" height=\"42\" title=\"\"><\/p><p>Alternativamente, podemos establecer el valor de la tendencia inicial utilizando la pendiente promedio de los dos primeros a\u00f1os, a saber:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-28465\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image008m.png\" sizes=\"(max-width: 333px) 100vw, 333px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image008m.png 333w, https:\/\/real-statistics.com\/wp-content\/uploads\/2019\/03\/image008m-300x40.png 300w\" alt=\"Tendencia inicial\" width=\"333\" height=\"44\" title=\"\"><\/p><p>Tenga en cuenta que si \u03b3 = 0, entonces el modelo de Holt-Winters es equivalente al modelo de tendencia lineal de Holt, y si \u03b2 = 0 y \u03b3 = 0, entonces el modelo de Holt-Winters es equivalente al modelo de suavizado exponencial simple.<\/p><p>Calcule los valores predichos de la serie temporal que se muestra en el rango C4:C19 de la figura utilizando el m\u00e9todo Holt-Winter con \u03b1 = 0,5, \u03b2 = 0,5 y \u03b3 = 0,5.<\/p><p>El resultado se presenta en la figura. Primero, calculamos s1, s2, s3, s4, donde c = 4, como se muestra en el rango F4:F7. Hacemos esto insertando la f\u00f3rmula =C4\/PROMEDIO(C$4:C$7) en la celda F4, resaltando el rango F4:F7 y presionando Ctrl-D.<\/p><p>A continuaci\u00f3n, calculamos uc y vc colocando la f\u00f3rmula =C7\/F7 en la celda D7 y el valor 0 en la celda E7.<\/p><p>Ahora insertamos la f\u00f3rmula =C$22*C8\/F4+(1-C$22)*(D7+E7) en la celda D8, la f\u00f3rmula =D$22*(D8-D7)+(1-D$22)*E7 en la celda E8, =E$22 *(C8\/D8)+(1-E$22)*F4 en la celda F8 y la f\u00f3rmula =(D7+E7)*F4 en la celda G8, luego resalte el rango D8:F19 y presione Ctrl-D.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21002 size-large\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9-1024x444.png\" alt=\"Holt-Winters multiplicativo\" width=\"1024\" height=\"444\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9-1024x444.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9-300x130.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9-768x333.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9-18x8.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters9.png 1075w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>Podemos usar Solver para determinar qu\u00e9 valores de alfa, beta y <a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/\">gama<\/a> proporcione el mejor ajuste de Holt-Winters para los datos de ejemplo.<\/p><p>Sin embargo, es probable que el enfoque de optimizaci\u00f3n que utiliza Excel Solver encuentre un m\u00ednimo local en lugar de un m\u00ednimo global. Por esta raz\u00f3n, los valores optimizados para alfa, beta y gamma son sensibles a los valores iniciales utilizados. Puede pedirle a Solver que pruebe diferentes valores iniciales para encontrar los valores de los par\u00e1metros que reducen el valor MAE.<\/p><p>Para hacer esto, seleccione Datos &gt; An\u00e1lisis | Solver y presione el bot\u00f3n Opciones en el cuadro de di\u00e1logo Solver. El cuadro de di\u00e1logo Solver contiene autom\u00e1ticamente los valores recopilados por la herramienta de an\u00e1lisis de datos de Pron\u00f3stico b\u00e1sico. Ahora elija la opci\u00f3n Multistart en la pesta\u00f1a GRG Nonlinear del cuadro de di\u00e1logo Opciones. El solucionador ahora se ejecutar\u00e1 varias veces utilizando diferentes valores iniciales, seleccionando los valores que produzcan el mejor resultado. El costo de esta opci\u00f3n son tiempos de ejecuci\u00f3n m\u00e1s lentos.<\/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-8101990 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8101990\" 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-37bdb27\" data-id=\"37bdb27\" 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-e010b14 elementor-widget elementor-widget-heading\" data-id=\"e010b14\" 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=\"Methode-additive-Holt-Winters\"><\/span>M\u00e9todo aditivo de Holt-Winters<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-4bccbb7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bccbb7\" 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-d125351\" data-id=\"d125351\" 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-0501e80 elementor-widget elementor-widget-text-editor\" data-id=\"0501e80\" 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>El modelo aditivo de Holt-Winters es id\u00e9ntico al modelo multiplicativo, excepto que la estacionalidad se considera aditiva. Esto significa que el valor previsto para cada elemento de datos es la suma de los componentes de referencia, tendencia y estacional. La suma de los componentes de estacionalidad para c per\u00edodos consecutivos es aproximadamente 1.<\/p><p>El enfoque recursivo del modelo aditivo es<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31445 size-medium\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image189-300x23.png\" sizes=\"(max-width: 300px) 100vw, 300px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image189-300x23.png 300w, https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image189.png 397w\" alt=\"Nivel de aditivo\" width=\"300\" height=\"23\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31446\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image190-300x30.png\" sizes=\"(max-width: 240px) 100vw, 240px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image190-300x30.png 300w, https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image190.png 314w\" alt=\"Tendencia aditiva\" width=\"240\" height=\"24\" title=\"\"><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-38170\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2022\/08\/image014.png\" alt=\"\" width=\"233\" height=\"24\" title=\"\"><\/p><p>donde 0 \u2264 \u03b1 \u2264 1, 0 \u2264 \u03b2 \u2264 1 y 0 \u2264 \u03b3 \u2264 1.<\/p><p>Las predicciones para los elementos de datos yi est\u00e1n dadas por<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31448\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image192.png\" alt=\"Previsi\u00f3n aditiva\" width=\"194\" height=\"27\" title=\"\"><\/p><p>Para pron\u00f3sticos en tiempos futuros, utilizamos el formulario<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31449\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/08\/image193.png\" alt=\"Previsi\u00f3n aditiva futura\" width=\"220\" height=\"27\" title=\"\"><\/p><p>\u00a0donde h\u2032 =INT((h\u20131)\/c)+1. Una versi\u00f3n alternativa del t\u00e9rmino de estacionalidad es:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33930\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image036.png\" sizes=\"(max-width: 290px) 100vw, 290px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2021\/06\/image036.png 350w, https:\/\/real-statistics.com\/wp-content\/uploads\/2021\/06\/image036-300x30.png 300w\" alt=\"T\u00e9rmino de estacionalidad alternativo\" width=\"290\" height=\"29\" title=\"\"><\/p><p>Con base en esta versi\u00f3n del t\u00e9rmino de estacionalidad, tenemos la siguiente forma alternativa de las ecuaciones recursivas:<\/p><p><a href=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image037.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33931\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image037.png\" alt=\"T\u00e9rmino u_i alternativo\" width=\"191\" height=\"27\" title=\"\"><\/a><\/p><p><a href=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image038.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33932\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image038.png\" alt=\"T\u00e9rmino v_i alternativo\" width=\"142\" height=\"27\" title=\"\"><\/a><\/p><p><a href=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image039.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33933\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image039.png\" alt=\"T\u00e9rmino alternativo s_i\" width=\"124\" height=\"27\" title=\"\"><\/a><\/p><p><a href=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image040.png\" rel=\"nofollow noopener\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-33934\" src=\"https:\/\/www.real-statistics.com\/wp-content\/uploads\/2021\/06\/image040.png\" alt=\"t\u00e9rmino y_i\" width=\"233\" height=\"27\" title=\"\"><\/a><\/p><p>Pronostique los valores de y para 2014 (es decir, los pr\u00f3ximos cuatro trimestres) utilizando el m\u00e9todo aditivo de Holt-Winter basado en datos del rango E4:F19 de la figura utilizando valores alfa, beta y gamma que minimizan la estad\u00edstica MSE.<\/p><p>Este es el mismo problema que el ejemplo del m\u00e9todo multiplicativo de Holt-Winters, excepto que ahora necesitamos aplicar el m\u00e9todo aditivo.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21003 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters10.png\" alt=\"Pron\u00f3stico de aditivos de Holt-Winters\" width=\"964\" height=\"513\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters10.png 964w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters10-300x160.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters10-768x409.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/holt-winters10-18x10.png 18w\" sizes=\"(max-width: 964px) 100vw, 964px\" \/><\/p><p>Podemos calcular el error est\u00e1ndar y los intervalos de predicci\u00f3n para los pron\u00f3sticos del modelo aditivo de Holt-Winters como se describe en Intervalo de confianza de suavizado exponencial, excepto que ahora el error est\u00e1ndar de k pasos adelante es<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31263\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/07\/image184.png\" alt=\"Error est\u00e1ndar de Holt-Winter\" width=\"220\" height=\"67\" title=\"\"><\/p><p>o<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31264 size-medium\" src=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/07\/image185-300x44.png\" sizes=\"(max-width: 300px) 100vw, 300px\" srcset=\"https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/07\/image185-300x44.png 300w, https:\/\/real-statistics.com\/wp-content\/uploads\/2020\/07\/image185.png 403w\" alt=\"F\u00f3rmulas de error est\u00e1ndar\" width=\"300\" height=\"44\" title=\"\"><\/p><p>Los errores est\u00e1ndar y los intervalos de predicci\u00f3n en la figura se calculan exactamente igual que para la tendencia lineal de Holt (consulte el intervalo de confianza de la tendencia lineal de Holt), con la excepci\u00f3n de la celda J26, ya que es una entrada donde c|i-1. La f\u00f3rmula en la celda J26 es<\/p><p>=22 K$*SQRT((K25\/K$22)^2-1+(F$30*(1+(FILA(J26)-FILA(J$22))*G$30+(1-F$30)*H$30) )^2+1)<\/p><p>El t\u00e9rmino (1-F$30)*H$30 en esta f\u00f3rmula no se encuentra en otras f\u00f3rmulas de error est\u00e1ndar (aunque dicho t\u00e9rmino se incluye en los errores est\u00e1ndar de avance de 5 pasos, avance de 9 pasos, avance de 13 pasos, etc.).<\/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 M\u00e9todo multiplicativo de Holt-Winters As\u00ed funciona el m\u00e9todo multiplicativo de Holt-Winters o triple suavizado. Suavizado exponencial simple \/ Suavizado exponencial\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-20986","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/20986","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=20986"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/20986\/revisions"}],"predecessor-version":[{"id":21007,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/20986\/revisions\/21007"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/20753"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=20986"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}