[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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