How much data is needed to properly fit a GARCH(1,1) model?

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#### Best Answer

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.

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