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.christo...@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-boun...@r-project.org [mailto:r-help-boun...@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 > > > _________________________________________________________________ > O Windows Live ajuda-o a manter-se em contacto com todos os seus amigos, > num > ss local. > > http://www.microsoft.com/portugal/windows/windowslive/products/social-networ > k-connector.aspx<http://www.microsoft.com/portugal/windows/windowslive/products/social-networ%0Ak-connector.aspx> > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
