GARCH(1,1) something like
Follow the example in tseries, we can simulated a GARCH(0,2), n <- 1100
a <- c(0.1, 0.5, 0.2) # ARCH(2) coefficients
e <- rnorm(n) x <- double(n)
x[1:2] <- rnorm(2, sd = sqrt(a[1]/(1.0-a[2]-a[3]))) for(i in 3:n) # Generate ARCH(2) process
{
x[i] <- e[i]*sqrt(a[1]+a[2]*x[i-1]^2+a[3]*x[i-2]^2)
}
x <- ts(x[101:1100])
and x is a GARCH(0,2).
But, I would like to know how to simulated a GARCH(1,2) ?
n <- 1100 a <- c(0.1, 0.2, 0.7)
e <- rnorm(n) x <- double(n)
v <- double(n)
v[1] <- a[1]/(1.0-a[2]-a[3]) x[1] <- rnorm(1, sd = sqrt(v[1]))
for(i in 2:n) {
v[i] <- a[1]+a[2]*x[i-1]^2+a[3]*v[i-1]
x[i] <- e[i]*sqrt(v[i])
}x <- ts(x[101:1100]) x.garch <- garch(x, order = c(1,1)) summary(x.garch)
and accordingly the GARCH(1,2)
best Adrian
-- Dr. Adrian Trapletti Trapletti Statistical Computing Wildsbergstrasse 31, 8610 Uster Switzerland Phone & Fax : +41 (0) 1 994 5631 Mobile : +41 (0) 76 370 5631 Email : mailto:[EMAIL PROTECTED] WWW : http://trapletti.homelinux.com
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