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 -- View this message in context: http://r.789695.n4.nabble.com/ARCH-modelling-MA-process-tp4632535.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
