{"id":2959,"date":"2021-09-21T10:21:35","date_gmt":"2021-09-21T10:21:35","guid":{"rendered":"https:\/\/ricovictor.com\/?p=2959"},"modified":"2026-01-29T21:45:57","modified_gmt":"2026-01-29T21:45:57","slug":"elegir-copulas-matematicas-en-r-ejemplo-en-forex","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2021\/09\/21\/elegir-copulas-matematicas-en-r-ejemplo-en-forex\/","title":{"rendered":"Elegir C\u00f3pulas Matem\u00e1ticas en R. Ejemplo en Forex"},"content":{"rendered":"\t\t
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Las c\u00f3pulas son distribuciones Multivariantes<\/strong> que sirven para medir la dependencia que puede haber entre muchas variables. Son una alternativa que busca corregir los errores o problemas que tiene el coeficiente de Correlaci\u00f3n.<\/strong> Gracias a ellas se consigue modelar la dependencia entre variables fuera de lo estrictamente lineal y sali\u00e9ndonos del mundo gaussiano.<\/p>

En este video te mostrar\u00e9 un m\u00e9todo para poder elegir que c\u00f3pulas matem\u00e1ticas se adaptan mejor a un determinada variable, en este caso usando el mercado Forex.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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CODIGO R DEL VIDEO<\/strong><\/p>

\u00a0<\/p>

#VIDEO COPULAS FOREX<\/p>

#Video Elecci\u00f3n de C\u00f3pulas<\/p>

#Son distribuciones Multivariantes que sirven para dependencia que puede haber entre muchas variables
#Son una alternativa que busca corregir los errores o problemas que tiene el coeficiente de Correlaci\u00f3n
#Se consigue modelar la dependencia entre variables fuera de lo estrictamente lineal y sali\u00e9ndonos del mundo gaussiano<\/p>


#install.packages(\u00abquantmod\u00bb)
library(quantmod)
#install.packages(\u00abtseries\u00bb)
library(tseries)
#install.packages(\u00abfImport\u00bb)
library(fImport)<\/p>

getSymbols(\u00abCADCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abAUDNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abAUDUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURGBP=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURJPY=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-12-18\u00bb)
getSymbols(\u00abEURUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abGBPCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abNZDCAD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)<\/p>

#precios de cierre<\/p>

CADCHF= `CADCHF=X`[,4]
AUDNZD= `AUDNZD=X`[,4]
AUDUSD= `AUDUSD=X`[,4]
EURCHF= `EURCHF=X`[,4]
EURGBP= `EURGBP=X`[,4]
EURJPY= `EURJPY=X`[,4]
EURNZD= `EURNZD=X`[,4]
EURUSD= `EURUSD=X`[,4]
GBPCHF= `GBPCHF=X`[,4]
NZDCAD= `NZDCAD=X`[,4]<\/p>

\u00a0<\/p>

?returns<\/p>

#FOREX<- cbind(USDTRY,USDSGD,USDHKD,USDMXN,USDNOK,USDSEK,USDDKK,EURSEK,EURNOK,EURNZD,NZDJPY,NZDCHF,EURUSD,GBPUSD,USDCHF,NZDUSD,EURAUD,GBPNZD,USDCAD,USDJPY,AUDCAD,CHFJPY,EURMXN,AUDNZD,AUDUSD,EURNZD,EURGBP,GBPCAD,GBPAUD,GBPJPY,EURCAD,AUDJPY,EURJPY,GBPCHF,EURCHF,NZDCAD,CADCHF)<\/p>

FX1=cbind(CADCHF,AUDNZD,AUDUSD,EURCHF,EURGBP,EURJPY,EURNZD,EURUSD,GBPCHF,NZDCAD)<\/p>


#Caluclamos los retornos y x 100 para calcularlos en %<\/p>

FX1=returns(FX1)
FX1=100*FX1[,1:ncol(FX1)]
FX<-as.timeSeries(FX1)
FX<-na.omit(FX)
head(FX)<\/p>


plot(FX)
head(FX)<\/p>

EURUSD_r <- FX[,8]
EURGBP_r <- FX[,5]<\/p>

media_eurusd<-mean(EURUSD_r)
media_eurgbp<-mean(EURGBP_r)
desv_eurusd<- sd(EURUSD_r)
desv_eurgbp<- sd(EURGBP_r)<\/p>

# Ajuste de c\u00f3pulas con paquete <copula>
#—————————————-<\/p>

install.packages(\u00abcopula\u00bb) # hacer esto una sola vez<\/p>

library(copula) # cargar paquete instalado al inicio de cada sesi\u00f3n en R<\/p>

### Normal de dos en dos sacando el AIC al final<\/p>

set.seed(6) # for reproducibility<\/p>

#normal.cop <- normalCopula(c(0.5), dim=2, dispstr=\u00bbun\u00bb)
#x <- rCopula(n, normal.cop) # \u00abtrue\u00bb observations (simulated)
#u <- pobs(x)<\/p>


# pseudo-observations<\/p>

# 1 Tenemos que crear una matrix 2 *2 para cada combinacion de variables<\/p>

# 2 Esa matriz la llamaremos \u00abx\u00bb<\/p>

# 3.Para crear la c\u00f3pula usaremos las pseudo observaciones de x, para que no
# nos de error ni salgan valores negativos<\/p>

# Comenzamos por orden con el Variable 1 y 2. Luego habr\u00e1 que hacer
# 1 y 3, 1 y 4 …….<\/p>

# probar 3 copulas = normal, t student y gumbell
# crea aic
# mirar la que tiene menor aic<\/p>


res11<- EURUSD_r #Variable 1
res22<- EURGBP_r #variable 2<\/p>

nn<- length(res11) # n\u00famero de filas de la matriz = longiutd de la varialbe
columnas<- 2 # Como la c\u00f3pula ser\u00e1 BI variada aqu\u00ed es 2<\/p>

x<- matrix(c(res11,res22),nn,columnas) #
u<- pobs(x)<\/p>

# Fijamos la COpula por el m\u00e9todo Maxima Verosimilitud(likehood)(ML)<\/p>

fit.ml <- fitCopula(normalCopula(dim=2, dispstr=\u00bbun\u00bb), u, method=\u00bbml\u00bb, traceOpt=TRUE)
#?fitCopula<\/p>

summary(fit.ml)
confint(fit.ml)
confint(fit.ml, level = 0.999)<\/p>

Estimador<- fit.ml@estimate # Estimate
Error_est<-fit.ml@var.est # Error est\u00e1ndar
Log_ver<-fit.ml@loglik # Valor m\u00e1xima verosimilutd<\/p>

Error_est
Log_ver<\/p>

# CALCULO DE CRITERIO DE AKAIKE(AIC) Y EL BIC<\/p>

# Lo hacemos a mano con la F\u00f3rmula<\/p>

# AIC <- -2*log-likelihood + k * npar<\/p>

aic<- -2*Log_ver + 2*1 #-2*log-likelihood + k*npar
aic<\/p>

bic <- -2*Log_ver + log(nn)* 1 #-2*log-likelihood + k*npar
bic<\/p>

#copula normal eurgbp eurusd = -36.06<\/p>


## COPULAS DE T STUDENT<\/p>

# Fijamos la COpula t studente m\u00e9todo M\u00e1xima Verosimilitud<\/p>

tc.ml <- fitCopula(tCopula(dim=2, dispstr=\u00bbun\u00bb), u, method=\u00bbml\u00bb)
summary(tc.ml)
confint(tc.ml)
confint(tc.ml, level = 0.999)<\/p>

Estimador_t<-tc.ml@estimate
Error_est_t<-tc.ml@var.est
Log_ver_t<-tc.ml@loglik<\/p>

# Sacamos AIC y BIC<\/p>

#-2*log-likelihood + k*npar<\/p>

aic_t <- -2*Log_ver_t + 2* 1
bic_t<- -2*Log_ver_t + log(nn)* 1<\/p>

aic_t
bic_t<\/p>

## COPULA DE GUMBELL ( arquimediana)<\/p>

\u00a0<\/p>

fit.ml <- fitCopula(gumbelCopula(), u, method=\u00bbml\u00bb)
summary(fit.ml)<\/p>

Estimador_gumbell<- fit.ml@estimate # Estimate
Error_est_gumbell<-fit.ml@var.est # Error est\u00e1ndar
Log_ver_gumbell<-fit.ml@loglik # Valor m\u00e1xima verosimilutd<\/p>

Error_est_gumbell
Log_ver_gumbell<\/p>

# CALCULO DE CRITERIO DE AKAIKE(AIC) Y EL BIC
# Lo hacemos a mano con la F\u00f3rmula<\/p>

# AIC <- -2*log-likelihood + k * npar<\/p>

aic_gumbell<- -2*Log_ver_gumbell + 2*1 #-2*log-likelihood + k*npar
aic_gumbell<\/p>

bic_gumbell <- -2*Log_ver_gumbell + log(nn)* 1 #-2*log-likelihood + k*npar
bic_gumbell<\/p>

\u00a0<\/p>

aic #normal
aic_t
aic_gumbell<\/p>

# 1 t student 2 normal 3 gumbell<\/p>

bic
bic_t
bic_gumbell<\/p>

##<\/p>


#simulaciones copula<\/p>

copula_sim <- rCopula(1000,tc.ml@copula)<\/p>

# Gr\u00e1ficos de dispersi\u00f3n de las pseudo-observaciones simuladas<\/p>

#dev.new(); par(mfrow = c(1, 2))
plot(copula_sim, main = \u00abC\u00f3pula t\u00bb)<\/p>

hist(copula_sim[,2])<\/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":"

Las c\u00f3pulas son distribuciones Multivariantes que sirven para medir la dependencia que puede haber entre muchas variables. Son una alternativa que busca corregir los errores o problemas que tiene el coeficiente de Correlaci\u00f3n. Gracias a ellas se consigue modelar la dependencia entre variables fuera de lo estrictamente lineal y sali\u00e9ndonos del mundo gaussiano. En este …<\/p>\n

Elegir C\u00f3pulas Matem\u00e1ticas en R. Ejemplo en Forex<\/span> Leer m\u00e1s »<\/a><\/p>\n","protected":false},"author":1,"featured_media":2961,"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":"\nElegir C\u00f3pulas Matem\u00e1ticas en R. Ejemplo en Forex - 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\/2021\/09\/21\/elegir-copulas-matematicas-en-r-ejemplo-en-forex\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Elegir C\u00f3pulas Matem\u00e1ticas en R. Ejemplo en Forex - V\u00edctor A. Rico \u2014 Econometr\u00eda y Finanzas Cuantitativas\" \/>\n<meta property=\"og:description\" content=\"Las c\u00f3pulas son distribuciones Multivariantes que sirven para medir la dependencia que puede haber entre muchas variables. Son una alternativa que busca corregir los errores o problemas que tiene el coeficiente de Correlaci\u00f3n. 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