# 5 .4 GARCH models . - PowerPoint PPT Presentation

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5 .4 GARCH models. ARCH(m ). GARCH( m.r ). A martingale difference series, E( y t |Y t-1 } = 0 “Learning a potential function …”. Cov not 0 generally. postscript(file="arch. ps ",paper="letter", hor =FALSE) par( mfrow =c(2,1)) library( tseries ) set.seed (28112006)

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5 .4 GARCH models .

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5.4 GARCH models.

ARCH(m)

GARCH(m.r)

A martingale difference series,

E(yt |Yt-1 } = 0

“Learning a potential function …”

Cov not 0 generally

postscript(file="arch.ps",paper="letter",hor=FALSE)

par(mfrow=c(2,1))

library(tseries)

set.seed(28112006)

a0<-1;a1<-.75

ylast<-1;Y<-ylast

Sig<-NULL

for(i in 1:250){

sig2<-a0+a1*ylast**2

y<-sqrt(sig2)*rnorm(1)

ylast<-y

Y<-c(Y,y)

Sig<-c(Sig,sqrt(sig2))

}

plot(Y,type="l",main="Data",xlab="time",ylab="",las=1)

plot(Sig,type="l",main="Sig",xlab="time",ylab="",las=1)

acf(Y,main="acf of data",xlab="lag",ylab="",las=1)

acf(Y**2,main="acf of data-squared",xlab="lag",ylab="",las=1)

graphics.off()