# [R] question about GARCH - newbie question

From: oliver wee <islandboy1982_at_yahoo.com>
Date: Sun 19 Feb 2006 - 02:52:48 EST

hello,
I have been looking at multiple websites on GARCH and have looked at some books and I am getting contradictory models given for GARCH.

If I use the GARCH function to fit my model, I am confused as to what the coefficents given refer to.

For example if I fit a GARCH(1,1) model, GARCH will give me three coefficients Ao, Ai, and Bi

I know Ao refers to the constant of the model. But what about Ai and Bi?

One website I looked at says the model for GARCH is: 1) S^2t = Ao + Ai S^2 t-1 + Bi E^2 t-1 + Et
(sigma squared sub t = a sub 0 + a sub 1 sigma squared
sub t-1 + b sub 1 epsilon squared sub t-1 + epsilon sub t)
while a book I was reading says the general model is 2) S^2t = Ao + Ai Y^2 t-1 + Bi S^2 t-1
(sigma squared sub t = a sub 0 + a sub 1 Y squared sub
t-1 + b sub 1 sigma squared sub t-1).

where Y refers to the data points of th time series S refers to the variance and E refers to the white noise component.

I am very confused by this.

Also, two other questions regarding GARCH, 1) How exactly do I forecast future values of my fitted GARCH model using R and how do I graph them? predict() won't work since it won't accept the n.ahead argument. (Assuming I already have fitted my original data set to an ARIMA model and have predicted future values using the predict() command).

2) This is not about R, but about GARCH in general. I just want to check if I understood GARCH correctly. For example, I have already found an ARIMA model to fit my original data set. In order for me to find the appropriate GARCH model to fit my data set, I have to get the acf of the squared values of my original data set (assuming the data set is stationary, that is, its acf show no significant correlations at all lags, but the acf of its squared values is not stationary). Once I get the acf of the squared values, I just compare this to the acf of arma(p,q) models- similar to how I was able to find my fitted ARIMA model? Is this correct? Also, once I have found the appropriate GARCH model, I can use this model to predict BOTH the future values of the data set and its variance? and these future values will be far different than the one given my my fitted ARIMA model?

I am sorry for the abundance of questions and I am pretty sure some of these questions sound pretty dumb. Its that I'm doing my study of time series mostly through self-study and I got really confused about GARCH. Thank you very much for your help.

R-help@stat.math.ethz.ch mailing list