[R] Question about copula-GARCH model

Jonas Malmros jonas.malmros at gmail.com
Fri Jun 20 23:52:57 CEST 2008

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;
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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