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5 .4 GARCH models .

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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  1. 5.4 GARCH models.

  2. ARCH(m) GARCH(m.r)

  3. A martingale difference series, E(yt |Yt-1 } = 0 “Learning a potential function …”

  4. Cov not 0 generally

  5. 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()

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