How much data is needed to properly fit 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) 

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.

| cite | improve this answer | |
  • $\begingroup$ @mpitkas - there is a similar recent post I entered in the Quant Finance forum at SE, and wonder if you would care to comment on fitting an AR(1)/GARCH(1,1) process to log-returns? Otherwise, the above is a very helpful response for simulation. $\endgroup$ – user32398 Nov 6 '13 at 12:55
  • $\begingroup$ @mpiktas, why is it surprising? Not to say it should not be, but a short note explaining this could be helpful. $\endgroup$ – Richard Hardy Aug 6 '17 at 9:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.