{"id":467,"date":"2020-05-08T13:53:10","date_gmt":"2020-05-08T13:53:10","guid":{"rendered":"https:\/\/ricovictor.com\/?p=467"},"modified":"2026-01-29T22:19:34","modified_gmt":"2026-01-29T22:19:34","slug":"independencia-entre-variables-con-matrices","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2020\/05\/08\/independencia-entre-variables-con-matrices\/","title":{"rendered":"Independencia entre variables con matrices"},"content":{"rendered":"\t\t
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\ud83d\udc4c En muchas ocasiones cuando vamos a crear alg\u00fan tipo de modelo estad\u00edstico<\/strong> y tenemos una gran cantidad de variables queremos saber si hay una relaci\u00f3n lineal muy fuerte entre ellas o por el contrario son independientes entre s\u00ed.<\/p>

\ud83d\udc68\u200d\ud83c\udfeb Dentro de las finanzas si quieres desarrollar una cartera<\/a> de inversi\u00f3n y c\u00f3mo es l\u00f3gico tu intenci\u00f3n es diversificar entre activos es posible que necesites filtrar de alguna manera al principio, porque es normal no saber que activos escoger al principio.<\/p>

Es por ello que puede ser \u00fatil utilizar alg\u00fan criterio espec\u00edfico que nos ayude de manera global a saber de todas nuestras variables cu\u00e1les son las m\u00e1s independientes entre ellas.<\/p>

\ud83d\ude03Una forma simple de ver \u00e9sto es utilizar uno de los conceptos que m\u00e1s utilizados en econometr\u00eda y matem\u00e1ticas<\/strong>,que son las matrices y determinantes.<\/p>

\ud83d\udc49Utilizando las matriz de correlaciones y haciendo el c\u00e1lculo del m\u00e1ximo determinante se puede crear un algoritmo<\/strong> que os permita estudiar la relaci\u00f3n de independencia existente entre vuestras variables.<\/p>

En \u00e9ste v\u00eddeo os explico c\u00f3mo pod\u00e9is hacerlo de manera pr\u00e1ctica. Yo uso los mercados financieros como ejemplo pero vosotros pod\u00e9is adaptarlo a otros campos. M\u00e1s abajo ten\u00e9is el c\u00f3digo usado tambi\u00e9n .\ud83d\udc47\ud83d\udc47<\/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

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C\u00d3DIGO EN R DEL V\u00cdDEO<\/strong><\/p>

\u00a0<\/strong><\/p>


####### INDEPENDENCIA LINEAL #######<\/p>


ges(\u00abtseries\u00bb)
library(tseries)
#install.packag
#install.packages(\u00abquantmod\u00bb)
library(quantmod)
#install.packaes(\u00abfImport\u00bb)
library(fImport)
#install.packages(\u00abexpm\u00bb)
library(expm)
#install.packages(\u00abfPortfolio\u00bb)
library(fPortfolio)
#install.packages(\u00abgtools)
library(gtools)<\/p>


# ————————————————-<\/p>


#### CALCULAR EL M\u00c1XIMO DETERMINANTE DE LA MATRIX DE CORRELACIONES<\/p>

#<\/p>

a<-c(1,0)
b<-c(0,1)
matrix(c(a,b),2,2)<\/p>


## DETERMINANTES = El determinante de una matriz es un escalar que s\u00f3lo se
#puede calcular si se trata de una matriz cuadrada,<\/p>


### Ejemplo matriz de correlaciones<\/p>


## Dentro de las correlaciones que haya entre nuestras variables, las vamos a ordenar
# para el obtener el m\u00e1ximo determinante<\/p>

getFX(c(\u00abEUR\/USD\u00bb,\u00bbGBP\/USD\u00bb))<\/p>

divisas1<-cbind(EURUSD,EURUSD) ### tabla eurusd
cor(divisas1)
det(cor(divisas1)) ## determinate 0 da lugar 0 maxima correlacion<\/p>

divisas<- cbind(EURUSD,GBPUSD)<\/p>

cor(divisas)<\/p>

det(cor(divisas)) #0.9744312 > 0 Al ser esto as\u00ed llegamos a la conclusi\u00f3n
# de que cuanto m\u00e1s alto es el determinante de la matriz menos es la correlaci\u00f3n o mayor
#la independencia de las variables<\/p>

### de 15 variables yo quiero saber las 10 m\u00e1s independientes<\/p>

CAC40=get.hist.quote(\u00ab^FCHI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
DAX=get.hist.quote(\u00ab^GDAXI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
#FTSEMIB=get.hist.quote(\u00abFTSEMIB.MI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2016-03-13″,end=\u00bb2017-03-13\u00bb)
FTSE=get.hist.quote(\u00ab^FTSE\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
SWISS=get.hist.quote(\u00ab^SSMI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
IBEX=get.hist.quote(\u00ab^IBEX\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
BELG=get.hist.quote(\u00ab^BFX\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
DOW=get.hist.quote(\u00ab^DJI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
NASDAQ=get.hist.quote(\u00ab^NDX\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
NIKKEI=get.hist.quote(\u00ab^N225″,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
SINGAPUR=get.hist.quote(\u00ab^STI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
HONG=get.hist.quote(\u00ab^HSI\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
SP500=get.hist.quote(\u00ab^GSPC\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
STOXX50=get.hist.quote(\u00ab^STOXX50E\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)
HOLANDA<- get.hist.quote(\u00ab^AEX\u00bb,quote=\u00bbClose\u00bb,start = \u00ab2019-01-07″,end=\u00bb2020-01-07\u00bb)<\/p>


iFX=na.omit(cbind(CAC40,DAX,SWISS,IBEX,DOW,NASDAQ,NIKKEI,SINGAPUR,HONG,STOXX50,SP500,HOLANDA))<\/p>


# Sacamos los retornos, comprobamos los resultados y los multiplicamos por 100 para tenerlo todo en %<\/p>

retornosFX = returns(iFX)
retornosFX = 100*retornosFX[ , 1:ncol(retornosFX)]
retornosFX<-na.omit(retornosFX)<\/p>

cor(retornosFX)<\/p>


# Buscamos todas las submatrices de X*X<\/p>

subTama\u00f1o = 5
determinantes = c()
choose(ncol(iFX), subTama\u00f1o) # N\u00ba de combinaciones totales
combinaciones = combinations(ncol(iFX), subTama\u00f1o)
head(combinaciones)<\/p>

filas = nrow(combinaciones)
progressBar = winProgressBar(title=\u00bbCalculando determinantes\u00bb, label=\u00bb0% calculado\u00bb, min=0, max=100, initial=0)
timestamp()
for (i in 1:filas) {

determinantes[i] = det(cor(iFX[,combinaciones[i,]]))
setWinProgressBar(progressBar, (i\/filas)*100, label=sprintf(\u00ab%d%% calculado\u00bb, round((i\/filas)*100)))
}
timestamp()
close(progressBar)
rm(i, subTama\u00f1o, filas)
head(determinantes)<\/p>

# Buscamos la combinaci\u00f3n de activos asociada al determinante m\u00e1s alto<\/p>

posMax = which(determinantes == max(determinantes))
posMax
combiMax = combinaciones[posMax, ]
combiMax<\/p>

# Creamos un nuevo data.frame con los X activos que nos interesen
jFX = data.frame(retornosFX[, combiMax])
names(jFX)<\/p>

head(iFX)<\/p>

#iFX=na.omit(cbind(CAC40,DAX,SWISS,IBEX,DOW,NASDAQ,NIKKEI,SINGAPUR,HONG,HOLANDA))<\/p>

\u00a0<\/strong><\/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":"

\ud83d\udc4c En muchas ocasiones cuando vamos a crear alg\u00fan tipo de modelo estad\u00edstico y tenemos una gran cantidad de variables queremos saber si hay una relaci\u00f3n lineal muy fuerte entre ellas o por el contrario son independientes entre s\u00ed. \ud83d\udc68\u200d\ud83c\udfeb Dentro de las finanzas si quieres desarrollar una cartera de inversi\u00f3n y c\u00f3mo es l\u00f3gico …<\/p>\n

Independencia entre variables con matrices<\/span> Leer m\u00e1s »<\/a><\/p>\n","protected":false},"author":19,"featured_media":471,"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":[59,60],"yoast_head":"\nIndependencia entre variables con matrices - V\u00edctor A. Rico \u2014 Econometr\u00eda y Finanzas Cuantitativas<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ricovictor.com\/index.php\/2020\/05\/08\/independencia-entre-variables-con-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Independencia entre variables con matrices - V\u00edctor A. 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