{"id":3245,"date":"2022-07-01T10:00:03","date_gmt":"2022-07-01T10:00:03","guid":{"rendered":"https:\/\/ricovictor.com\/?p=3245"},"modified":"2022-07-01T10:12:42","modified_gmt":"2022-07-01T10:12:42","slug":"entendiendo-el-modelo-arima-parte-1","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2022\/07\/01\/entendiendo-el-modelo-arima-parte-1\/","title":{"rendered":"Entendiendo el MODELO ARIMA | Parte 1"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"3245\" class=\"elementor elementor-3245\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-36cd62ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"36cd62ca\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-wide\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-500f8db6\" data-id=\"500f8db6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4de113ce elementor-widget elementor-widget-text-editor\" data-id=\"4de113ce\" 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>El Modelo <strong>ARIMA (Autoregresivo Integrado de Media M\u00f3vil)<\/strong> es un tipo de modelo econom\u00e9trico muy extendido para la predicci\u00f3n en series de tiempo. En este tutorial vamos a estudiar como se interpretan los resultados del modelo as\u00ed como se relacionan con la formula te\u00f3rica ayud\u00e1ndonos de Rstudio. Esta ser\u00e1 la primera parte de la explicaci\u00f3n que se dividir\u00e1 en 2 clases<\/p><p>Tambi\u00e9n abajo puedes copiar el <strong>c\u00f3digo<\/strong> usado en el v\u00eddeo.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-78df5cad\" data-id=\"78df5cad\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1161af58 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"1161af58\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\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-2d095aa4 elementor-widget elementor-widget-video\" data-id=\"2d095aa4\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/UYDcSzoJdhU&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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-1b078a9b elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"1b078a9b\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a3dc6ff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a3dc6ff\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3f48027b\" data-id=\"3f48027b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fe9d11c elementor-view-stacked elementor-shape-circle elementor-widget elementor-widget-icon\" data-id=\"fe9d11c\" data-element_type=\"widget\" data-widget_type=\"icon.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-wrapper\">\n\t\t\t<div class=\"elementor-icon\">\n\t\t\t<i aria-hidden=\"true\" class=\"fas fa-arrow-circle-down\"><\/i>\t\t\t<\/div>\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-1e1ba271 elementor-widget elementor-widget-text-editor\" data-id=\"1e1ba271\" 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<h4>Codigo R del Video<\/h4><p>#INTERPRETACION ARIMA<\/p><p>#video Proceso Autoregresivo (AR)<\/p><p><br \/>#install.packages(\u00abquantmod\u00bb)<br \/>library(quantmod)<br \/>#install.packages(\u00abtseries\u00bb)<br \/>library(tseries)<br \/>#install.packages(\u00abforecast\u00bb)<br \/>library(forecast)<br \/>#install.packages(\u00abTSA\u00bb)<br \/>library(TSA)<br \/>#install.packages(\u00abQuandl\u00bb)<br \/>library(Quandl)<br \/>library(stats)<br \/>#install.packages(\u00ablmtest\u00bb)<br \/>library(lmtest)<\/p><p><br \/># INTERPRETACI\u00d3N ARIMA :<\/p><p><br \/># 3 COMPONENTES : AR &#8211; I- MA<\/p><p>#AR = Componente Autoregresivo<br \/>#I = Componente de Diferenciaci\u00f3n. N\u00famero de veces que la serie debe ser diferenciada para hacerla estacionaria<br \/>#MA = Componente de Media M\u00f3vil<\/p><p>#(Termino AR) ( TERMINO MA)<br \/>#Y[t] = constante + b1*Y[t-1] + e[t] + theta * e[t-1]<br \/><br \/><br \/># AR (AUTOREGRESIVO)<br \/><br \/>#Implica relaci\u00f3n de un valor de una serie en un punto del tiempo <br \/>#con sus propios valores previos.Tal relaci\u00f3n puede existir con cualquier orden de retraso(lag en ingl\u00e9s)<br \/><br \/># Mirar ejemplo en la tabla antes de la ecuaci\u00f3n<\/p><p># INTERPRETACION DE LA ECUACION<\/p><p># AR(1)<\/p><p># Y(t)= c + b1*Y(t-1) + e(t) donde e(t) ruido blanco ~ N(0,s^2)<\/p><p># AR(2) (como vimos en la tabla)<\/p><p># Y(t)= c + b1*Y(t-1) + B2*Y(t-2) + e(t)<\/p><p><br \/>#IMPORTANTE: \u00abc\u00bb dentro del Modelo<\/p><p># c = mu * (1 &#8211; b1 ) donde mu es la media de Y<\/p><p>\u00a0<\/p><p># Y(t)= mu * (1 &#8211; b1 ) + b1*Y(t-1) + e(t)<br \/># \u00abconstante\u00bb<\/p><p><br \/># de forma que al sustituir nos queda as\u00ed<\/p><p>\u00a0<\/p><p># y^[t] &#8211; mu = B1(Y[t-1]-mu) + e[t]<br \/><br \/><br \/>#y[t] = mu + (1 &#8211; B1) + b1*y[t-1] + e[t]<\/p><p>#Podremos ver el modelo escrito de 2 formas, pero interpretaci\u00f3n es la misma<\/p><p># 1. y^[t] &#8211; mu = B1(Y[t-1]-mu) + e[t]<\/p><p># 2. Y(t)= c + b1*Y(t-1) + e(t) <br \/><br \/>#########################################<br \/><br \/>#install.packages(\u00abquantmod\u00bb)<br \/>library(quantmod)<br \/>#install.packages(\u00abtseries\u00bb)<br \/>library(tseries)<br \/>#install.packages(\u00abforecast\u00bb)<br \/>library(forecast)<br \/>#install.packages(\u00abTSA\u00bb)<br \/>library(TSA)<br \/>#install.packages(\u00abQuandl\u00bb)<br \/>#library(Quandl)<br \/>library(stats)<br \/>#install.packages(\u00ablmtest\u00bb)<br \/>library(lmtest)<br \/><br \/><br \/>## HACEMOS MODELO AR(1)<br \/><br \/><br \/>## PRECIOS DE LAS ACCIONES<br \/><br \/>acciones &lt;- c(235,320,115,355,190,320,275,205,395,240,355,175,285,<br \/>200,290,220,400,275,185,370,255,285,250,300,225,285,<br \/>250,225,125,295,250,355,280,370,250,290,225,270,180,<br \/>270,240,275,225,285,250,310,220,320,215,260,190,295,<br \/>275,205,265,245,170,175,270,225,340,190,250,300,195)<br \/><br \/>plot(acciones,type=\u00bbl\u00bb)<br \/><br \/><br \/>adf.test(acciones) # test de raiz unitaria<br \/><br \/>#EL MODELO ARIMA PIDE QUE LAS SERIES SEAN ESTACIONARIAS<br \/><br \/># REALIZAMOS UN MODELO AR(1) arima(1,0,0)<br \/><br \/>arima_acc &lt;- arima(acciones,order=c(1,0,0))<br \/>arima_acc<br \/><br \/>#? \u00bfC\u00f3mo saca el ARIMA los coeficientes que vemos en el SUMARIO?<br \/>#method = c(\u00abCSS-ML\u00bb, \u00abML\u00bb, \u00abCSS\u00bb)<br \/><br \/><br \/>?arima<br \/><br \/>coeftest(arima_acc)<br \/><br \/>z_value1&lt;- &#8211; 0.40472\/ 0.11329<br \/>z_value1<br \/>zvalue&lt;- 259.31594\/4.88598<br \/><br \/>summary(arima_acc)<br \/><br \/><br \/>residuos&lt;- arima_acc$residuals<br \/>betas = arima_acc$coef<br \/><br \/><br \/>coef_ar &lt;-betas[1]<br \/>intercepto &lt;- betas[2]<br \/><br \/>mean(acciones)<br \/><br \/>predict(arima_acc) # arima(1,0,0) serie acciones 285.3459<br \/><br \/>forecast(arima_acc)<br \/><br \/><br \/>#Calculo de los valores fijados reescribiendo ecuaci\u00f3n<br \/><br \/><br \/># Y(t)= mu * (1 &#8211; b1 ) + b1*Y(t-1) + e(t)<br \/><br \/>y_fijados = intercepto*(1- coef_ar) + coef_ar*lag(acciones,default=0)<br \/>y_fijados[1:64]<br \/><br \/><br \/><br \/>#Me falta poner el valor 1<br \/>fitted.values(arima_acc)<br \/><br \/># Hacemos una Predicci\u00f3n para el periodo 66 con predict<br \/><br \/>predict(arima_acc)<br \/><br \/># hacemos la predicci\u00f3n con la ecuaci\u00f3n escrita <br \/>#t-1<br \/>Predicci\u00f3n_t66 &lt;- intercepto*(1- coef_ar) + coef_ar*acciones[65]<br \/>Predicci\u00f3n_t66<br \/><br \/><br \/>### RECAPITULANDO<br \/><br \/># Hemos visto la ecuaci\u00f3n del Modelo AR, su interpretaci\u00f3n<br \/># y luego hemos comparado los resultados y predicci\u00f3n hechos por R<br \/># con los resultados que a nosotros nos da en la ecuaci\u00f3n escrita<br \/><br \/># as\u00ed como hemos apuntado los m\u00e9todos por los que Arima de R busca los <br \/>#coeficientes<br \/><br \/>#############################<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>El Modelo ARIMA (Autoregresivo Integrado de Media M\u00f3vil) es un tipo de modelo econom\u00e9trico muy extendido para la predicci\u00f3n en series de tiempo. En este tutorial vamos a estudiar como se interpretan los resultados del modelo as\u00ed como se relacionan con la formula te\u00f3rica ayud\u00e1ndonos de Rstudio. Esta ser\u00e1 la primera parte de la explicaci\u00f3n &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2022\/07\/01\/entendiendo-el-modelo-arima-parte-1\/\"> <span class=\"screen-reader-text\">Entendiendo el MODELO ARIMA | Parte 1<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":3247,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Entendiendo el MODELO ARIMA | Parte 1 - V\u00edctor A. 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