[R] Predict GARCH

[bogaso.christofer]

Suppose the GARCH(1,1) equation is :

Sigma[t]^2 = w + a* Sigma[t-1]^2 + b*r[t-1]^2

One step ahead forecast :
Sigma[t+1]^2 = w + a* Sigma[t]^2 + b*r[t]^2  All informations are available
here

Two step ahead forecast :
Sigma[t+2]^2 = w + a* Sigma[t+1]^2 + b*r[t+1]^2  
Here r[t+1] is not known at time "t" therefore is a r.v. Replacing this with
it's expected value as r[t+1]^2  = E[r[t+1]^2]  = sigma[t+1]^2, assuming
E[r[t+1]] = 0

Therefore Sigma[t+2]^2 = w + a* Sigma[t+1]^2 + b*r[t+1]^2  
                       = w + a* Sigma[t+1]^2 + b* Sigma[t+1]^2
                       = w + (a+b)* Sigma[t+1]^2

Carry on same procedure for next period forecast.
Hope this helps.


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Daniel Mail
Sent: 10 June 2009 18:55
To: r-help at r-project.org
Subject: [R] Predict GARCH



 



hello,
 
 
i was trying to predict values for a garch, so i did:
 
predict(fitgarch,n.ahead = 20)
 
but this doesn't work. Someone can tell me how to get the 20 values ahead of
a garch model.
 
 
thanks in advance


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