{"id":2997,"date":"2021-10-01T22:05:07","date_gmt":"2021-10-01T22:05:07","guid":{"rendered":"https:\/\/ricovictor.com\/?p=2997"},"modified":"2026-01-29T21:45:29","modified_gmt":"2026-01-29T21:45:29","slug":"teoria-de-valores-extremos-pareto-generalizada","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2021\/10\/01\/teoria-de-valores-extremos-pareto-generalizada\/","title":{"rendered":"Teor\u00eda de Valores Extremos| Pareto Generalizada"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2997\" class=\"elementor elementor-2997\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-55daf392 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"55daf392\" 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-727d90b1\" data-id=\"727d90b1\" 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-15fc7aaf elementor-widget elementor-widget-text-editor\" data-id=\"15fc7aaf\" 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><strong><span class=\"style-scope yt-formatted-string\" dir=\"auto\">La Teor\u00eda de Valores Extremos (EVT de sus siglas en ingl\u00e9s) es la rama de la estad\u00edstica que fija su an\u00e1lisis en los eventos asociados a las colas de la distribuci\u00f3n (Valores mayores y menores de la variable en concreto).<\/span><\/strong><\/p><p><span class=\"style-scope yt-formatted-string\" dir=\"auto\"> Normalmente, en <\/span>estad\u00edstica<span class=\"style-scope yt-formatted-string\" dir=\"auto\">, cuando hacemos alg\u00fan an\u00e1lisis nos solemos fijar en las parte central de los datos, descartando aquellos que son menos probables. Incluso muchas veces los datos m\u00e1s extremos se eliminan para que no interfieran en el resultado. Pero esta pr\u00e1ctica no siempre es buena, porque en su seg\u00fan que momentos estos datos pueden darnos informaci\u00f3n muy \u00fatil, incluso determinante.<\/span><\/p><p><span class=\"style-scope yt-formatted-string\" dir=\"auto\"> Particularmente es en esos datos extremos donde la Teor\u00eda de Valores Extremos trabaja. Si nos centramos en <\/span>finanzas<span class=\"style-scope yt-formatted-string\" dir=\"auto\">, por ejemplo en las series de precios ,como pueden ser los de las bolsa,forex,etc\u2026,esta teor\u00eda se puede usar para estudiar estos valores, y tener una mejor <strong>idea de la volatilidad y el riesgo<\/strong>. <\/span><\/p><p><span class=\"style-scope yt-formatted-string\" dir=\"auto\">En este video explico una de las formas para aplicar la teor\u00eda, que es mediante la <strong>Distribuci\u00f3n de <\/strong><\/span><strong>Pareto<span class=\"style-scope yt-formatted-string\" dir=\"auto\"> Generalizada. <\/span><\/strong><span class=\"style-scope yt-formatted-string\" dir=\"auto\">M\u00e1s abajo tienes el c\u00f3digo R usado<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3cd9f9dd elementor-view-stacked elementor-shape-circle elementor-widget elementor-widget-icon\" data-id=\"3cd9f9dd\" 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=\"far fa-hand-point-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\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-67f338da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"67f338da\" 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-63fa59f3\" data-id=\"63fa59f3\" 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-1bb5fd8c elementor-widget elementor-widget-video\" data-id=\"1bb5fd8c\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=00j8Ef40vR8&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\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-7f30b47 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7f30b47\" 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-324fd32\" data-id=\"324fd32\" 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-0741269 elementor-widget elementor-widget-text-editor\" data-id=\"0741269\" 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><strong>CODIGO R DEL VIDEO<\/strong><\/p><p>\u00a0<\/p><p>#Video Teor\u00eda Valores Extremos _ Pareto Generalizado<\/p><p>#install.packages(\u00abquantmod\u00bb)<br \/>library(quantmod)<br \/>#install.packages(\u00abtseries\u00bb)<br \/>library(tseries)<br \/>#install.packages(\u00abfImport\u00bb)<br \/>library(fImport)<\/p><p>getSymbols(\u00abCADCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abAUDNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abAUDUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abEURCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abEURGBP=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abEURJPY=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abEURNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abEURUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abGBPCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abNZDCAD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<br \/>getSymbols(\u00abGBPUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2012-01-01\u00bb)<\/p><p><br \/>#precios de cierre<\/p><p>CADCHF= `CADCHF=X`[,4]<br \/>AUDNZD= `AUDNZD=X`[,4]<br \/>AUDUSD= `AUDUSD=X`[,4]<br \/>EURCHF= `EURCHF=X`[,4]<br \/>EURGBP= `EURGBP=X`[,4]<br \/>EURJPY= `EURJPY=X`[,4]<br \/>EURNZD= `EURNZD=X`[,4]<br \/>EURUSD= `EURUSD=X`[,4]<br \/>GBPCHF= `GBPCHF=X`[,4]<br \/>NZDCAD= `NZDCAD=X`[,4]<br \/>GBPUSD= `GBPUSD=X`[,4]<\/p><p>plot(EURGBP,type=\u00bbl\u00bb) # serie precios en diario<\/p><p># sacar retornos<\/p><p>r_eurgbp &lt;-na.omit(returns(EURGBP))*100<\/p><p>plot(r_eurgbp,type=\u00bbl\u00bb)<\/p><p>hist(r_eurgbp)<\/p><p>#2 umbral<\/p><p>quantile(r_eurgbp,c(0.05,0.95))<\/p><p>plot(r_eurgbp,type=\u00bbl\u00bb)<\/p><p>abline(0.8273344,0,col=\u00bbred\u00bb)<br \/>abline(-0.7636476,0,col=\u00bbred\u00bb)<\/p><p><br \/>## calculariamos los excedentes<\/p><p>val_pos = r_eurgbp [r_eurgbp &gt; 0.8273344]<br \/>val_pos<\/p><p>plot(val_pos,type=\u00bbl\u00bb)<br \/>hist(val_pos)<\/p><p>excedente_pos= val_pos &#8211; 0.8273344<br \/>excedente_pos<\/p><p>hist(excedente_pos)<\/p><p><br \/>####### formula en r<\/p><p><br \/>#???install.packages(\u00abevir\u00bb)<\/p><p>library(\u00abevir\u00bb)<\/p><p>\u00a0<\/p><p>pareto= r_eurgbp # Para Cola Positiva<\/p><p>#r_eurgbp_neg = r_eurgbp*-1 # Para Cola Negativa<\/p><p>\u00a0<\/p><p>fit&lt;- gpd(pareto,threshold=0.8273344, nextremes=NA) # umbral y cantidad<br \/>fit<\/p><p>plot(fit$data,type=\u00bbl\u00bb) # datos que sobrepasan el umbral(cola)<br \/>hist(fit$data) #histograma cola<\/p><p>#?gpd.q<\/p><p>#plot(fit)<\/p><p>tp&lt;-tailplot(fit)<br \/>tp<\/p><p>#??tailplot<\/p><p># sacamos los 3 par\u00e1metros &#8211; localizaci\u00f3n, escala, forma<\/p><p>loc&lt;-tp$location <br \/>scal&lt;-tp$scale<br \/>shape&lt;-tp$shape<\/p><p><br \/>#Funci\u00f3n cuartil y estimate<\/p><p>#?gpd.q<\/p><p>#Percentil 99 al 99% de confianza<\/p><p>Estimate&lt;- gpd.q(tp, pp= 0.99, ci.p=0.99)<br \/>Estimate<\/p><p>\u00a0<\/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>La Teor\u00eda de Valores Extremos (EVT de sus siglas en ingl\u00e9s) es la rama de la estad\u00edstica que fija su an\u00e1lisis en los eventos asociados a las colas de la distribuci\u00f3n (Valores mayores y menores de la variable en concreto). Normalmente, en estad\u00edstica, cuando hacemos alg\u00fan an\u00e1lisis nos solemos fijar en las parte central de &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2021\/10\/01\/teoria-de-valores-extremos-pareto-generalizada\/\"> <span class=\"screen-reader-text\">Teor\u00eda de Valores Extremos| Pareto Generalizada<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":3002,"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>Teor\u00eda de Valores Extremos| Pareto Generalizada - V\u00edctor A. 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