# [R] CAPM-GARCH - Regression analysis with heteroskedasticity

barb mainzel89 at hotmail.com
Thu Nov 24 20:50:41 CET 2011

```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. ß_1 and a0 the coefficents and r2 the squared
returns:

Infinitive ARCH Model:
h<-ao*sum(ß_1^i)+a1*sum(ß_1^(i-1)*r2_{t-i})

How I used it in R:
sumofbeta<- ß_1^rep(1:length(r2)) # Beta-Seq sum(ß_1^i) for the sum of the
product
h<-a0*(1/1-ß_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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