R help - Nov 2011 - CAPM-GARCH - Regression analysis with heteroskedasticity

Hey Guys,

i want to do a CAPM-GARCH model. I didn?t find anything posted online. 
(If there is something - shame on me - i didn?t find it.)

My Problem: 	What is the difference if I let the residuals ?e? follow a
garch process  ? 
		How do I do my regression analysis now? I began reading about regression
analyis with 		heteroscedasticity, but didn?t get it.

So i started programming. 

First loading data with quantmod and applying a function to get continously
compounded returns
and squared returns. Looks good - stylised facts seems to be covered. 

Starting with GARCH:
I use a GARCH(1,1) but will use it as an infinite ARCH(1,1):
Let h be the variance. ?_1 and a0 the coefficents and r2 the squared
returns: 

Infinitive ARCH Model: 
	h<-ao*sum(?_1^i)+a1*sum(?_1^(i-1)*r2_{t-i}) 
	
How I used it in R:
	sumofbeta<- ?_1^rep(1:length(r2)) # Beta-Seq sum(?_1^i) for the sum of the
product
	h<-a0*(1/1-?_1)+a1*(t(sumofbeta)%*%r2)

Now i have my variance:

DOING THE CAPM:

Applying a simple regression analysis

ri <- alpha+beta*rm+e
e ~ N(0,h)
h is following the GARCH process decribed above

I don?t really get how my regression analysis changed when I change the
distribution of my residual ?e?. 
May be a dump question and somehow ashaming because it?s the  concept of
CAPM-GARCH =) but I have to admit I don?t get it.  

Thanks for your time and help 

Regards	Tonio


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Okay, it seems to work with Mahalanobis:
b = (X?S^?1X)?1X?S^?1Y minimizes the Mahalanobis-distance of Xb to Y .
And S is the covariance-matrix. 

cov = a0+a1x_{n-1}*y_{n-1}+?*cov{n-1}
But shouldn?t it be the covariance of the residuals?

Anyone experiences with that?

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