[R] Question about copula-GARCH model

From: Jonas Malmros <jonas.malmros_at_gmail.com>
Date: Fri, 20 Jun 2008 23:52:57 +0200


Hello everyone,

I am learning about copulas and also do some MATLAB/R coding to get better understanding of how copulas work. Recently I have started coding simple copula-GARCH models, that is I fit say AR(1)-GARCH(1,1)-normal models to univariate time series, and then I want to fit the copula (two-stage procedure).

What I have problem with is connecting these two estimation stages. After I have estimated AR-GARCH univariate models, what do I take from these models and put into log-likelihood estimation of the copula? Do I take residuals from AR-GARCH models, or do I use estimated parameters of these models to produce samples that I then use in copula estimation stage?

I read a few papers that use copula-GARCH models, but it is not clear from them how to estimate copula model.
In one of the papers it says: "Let u=F(x; theta(x)) and v=F(y; theta(y)), where theta(x) and theta(y) are the vectors of parameters of each marginal distribution..." and then one uses u and v in copula log-likelihood minimization.
I am so embarassed, but I still do not get it. If I estimated the GARCH model parameters, how do I get these F(x; theta(x)) and F(y; theta(y))?
Probably very simple and totally obvious thing, but I just do not get it. :-( Could you please help me understand? How do I do it in MATLAB or R?

THanks in advance!

-- 
Jonas Malmros

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Received on Sat 21 Jun 2008 - 05:12:03 GMT

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