Question about copula-GARCH models

#1
Hello everyone,

I am learning about copulas and also do some MATLAB 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? :confused:

I read a few papers that use copula-GARCH models, but it is not clear from them how to estimate copula model. :( One paper stated that after AR-GARCH univariate model is estimated, I get parameters THETA(x), where x is the time series used in estimation. And then I should estimate F(x, THETA(x)), that is cdf. :confused:
I still do not get it. :eek:
Probably very simple and 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!
/Sergey