[R] ARCH modelling/MA process

[and_mue]

Hi all

ARCH modelling


I have a problem now on how to proceed with further steps in my analysis. I
did a linear OLS regression 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)

The problem is now that I want to analyse the excess return for a given
period. 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... 
/(FOR INFORMATION: excess return without ammendements for ARCH effects is
given as: êt=Ri,t-alpha(from regression)-beta(from regression)*Rm,t)/

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
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100573 ). It is
described as follows:

Ri=alpha(arch)+beta(arch)*Rm,i+et
et=thetat*sqrt(h)
h=lamda(0)+lamda(1)*e(t-1)^2  ##e are the residuals of the ols regression

Thus my question is now: How can I regress this?

Ri=alpha(arch)+beta(arch)*Rm,i+thetat*sqrt(h) ## This seems not to work as
it calculates an additional errorterm. Also the parameter theta changes over
time. Thus the problem is on how I should estimate this one.... 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).

MA Process:

I have for example an MA(1) process. This mean that ut=et+theta*et-1
Thus the linear regression gets (also excess return on the left hand side):
et=Ri,t-alpha-beta*Rm,i-theta*et-1
The problem is now that et depends on et-1. I want to start with et-1=0,
thus I cant do this with one formula. And typing this in for 180 days is
simply to time consuming. 

Any suggestions on that Problem? One solution would be to do this with
excel.

Thanks and kind regards
Andi


Kind regards
Andi



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