Hi
I have a problem on how to proceed with further steps in my analysis. I did
a linear OLS regression (ri,t=alpha*beta*rm,t+et) with my daily data of
stock and index returns. There is now the problem of arch in my error terms.
Thus I used the following r command:
/garch(resid_desn, order=c(0,2)) ## This ARCH(2) process seems to fit the
best after trial and error. Consequently, I get there three a's.
(resid_desn are the residuals of the ols regression of the company desn) /
And now I am stuck. For further analysis I want to estimate new alphas and
betas which do incorporate this ARCH effect (thus including all the a's in
some way). There is a paper which does this in a simple manner (see page 12
and 13 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100573). It is
described as follows:
/Ri=alpha(arch)+beta(arch)*Rm,i+et ## equation one
et=ut*sqrt(h)
h=lamda(0)+lamda(1)*e(t-1)^2+lamda(2)*e(t-2)^2 ##e are the residuals of the
ols regression /
I don't know how I should include these a's in my linear regression to
address this problem and get new alphas and betas. I tried to substitute and
rearrange (h can be calculated from the ols and garch output, then I
substitute et in equation one with ut*sqrt(h) and divide the whole equation
by sqrt(h)). After the regression procedure there is still significant ARCH
effect in my model. I don't know if dividing is the right step but without
this, r would incorporate another error term. My assumption is that ut is an
error term.
The purpose of this is to estimate excess returns after the estimation
period.
(FOR INFORMATION: excess return without ammendements for ARCH effects is
given as: ?t=Ri,t-alpha-beta*Rm,t)
Thus my question is now: How can I regress this to get results without ARCH
effect?
I hope there is a solution for this problem or some hints on how I can use
the output of the garch model for my linear regression and the estimation of
new alphas and beta (with consideration of ARCH effects). *Help is really
appreciated!!!*
Kind regards
Andi
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