R help - Jun 2008 - Question about copula-GARCH model

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

A simple approach is to assume that dependence structure between
variables (which is characterized by copula) is constant throughout
the process. In this case, you may apply log-likelihood estimation of
copula parameters to ranked AR-GARCH process residuals.

A more complicated approach is to invent a model of how copula
parameters depend on the previous values of the process. This *might*
provide a better description of some empirical effects. But in
reality, these models are not reliable enough, because you are likely
to deal with many more parameters than in univariate case, and there
is no general way to estimate the parameters of copula evolution.
However, attempts are still made (see for example package mgarchBEKK).

Andrey