So christofer proved (carry on the same procedure infinite times) that the
forecast of the variance converge to the long run variance when a+b<1

   E(Sigma[t+2]^2) = w/(1-a-b) + [(a+b)^t]* Sigma[t+1]^2

Therefore when you predict n.ahead = 20 it must to converge to the long run
variance. It can be fast depending on the data.

Regards,

Marlene.



2009/6/10 bogaso.christofer <bogaso.christofer@gmail.com>

> 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@r-project.org [mailto:r-help-bounces@r-project.org]
> On
> Behalf Of Daniel Mail
> Sent: 10 June 2009 18:55
> To: r-help@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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