Solved – Fitting a GARCH(1,1) model

Depends on the coefficients. Simple Monte-Carlo analysis suggests that a lot, about 1000, which is quite surprising.

N <- 1000 n <- 1000+N a <- c(0.2, 0.3, 0.4)  # GARCH(1,1) coefficients e <- rnorm(n)   x <- double(n) s <-double(n) x[1] <- rnorm(1)  s[1] <- 0 for(i in 2:n)  # Generate GARCH(1,1) process {   s[i] <- a[1]+a[3]*s[i-1]+a[2]*x[i-1]^2       x[i] <- e[i]*sqrt(s[i]) } x <- ts(x[1000+1:N]) x.garch <- garchFit(data=x)  # Fit GARCH(1,1)  summary(x.garch)      

I modified example code from garch from tseries package, but I used garchFit from fGarch package, since it seemed that it gave better results. I used 1000 values for burn-in.