Package fGarch

[Pierre Chaussé]

Hi,

I am writing a guide for my financial econometrics class and I found a 
mistake in the method predict() that comes with the package fGarch.  It 
does not predict correctly because it does not use the predict.Arima  
method correctly. In arima() the constant term is not an intercept but a 
mean.  For exemple, if we have the following AR(1) process:

X(t) = 6 + 0,9 X(t-1) + e(t)

What arima() calls "intercept" is not the 6 but the mean of X which is 
6/(1-0,9)=60.  So if we know the model and want to predict it, we can, 
as it is done in methods-predict.R that comes in fGarch, create an arima 
object and use predict() on it. But we have to provide the mean and not 
the intercept. For our exemple we can do:

ARIMA = arima(x,order=c(1,0,0),init=(0,9,60),optim.control=list(maxit=0))
and
predict(ARIMA,n.ahead)

The problem is that garchFit() computes the intercept and not the mean 
(which I thing it is better) and when we apply predict() on the object 
that it creates, it provides the intercept to arima() instead of the mean. 

In line 128 of methods-predict.R, you should replace mu by the mean 
which is mu/(1-sum_of_ar_coef).

One more thing. Since fGarch computes conditional variance, why the 
predict() method does not compute the conditional mean square errors of 
the prediction instead of the unconditional ones. In finance, the former 
would be more appropriate.

Thank you

Pierre Chaussé
Université du Québec à Montréal
 http://www.er.uqam.ca/nobel/k34115/