I need to replicate what Huang and al (2009)* did without using built-in functions in R. What I'm struggling with is how to forecast returns for my two data samples. I've found the GARCH specs and Copula specs. I can forecast volatility using GARCH but I also have to add the dependent correlation that should stem from the copulas (we're assuming correlation is non-static). I don't know how to forecast correlation every day.
More details : We have 2 assets to construct an equal-weighted portfolio. We model their volatility according to a GARCH(1, 1), then model the residuals with 4 different copulas.In this first part, we should be able to identify which copula is most accurate in its fit. We now need to forecast the portfolio's return for n iterations. I don't have a problem with forecasting using GARCH, I have no clue how to forecast the correlation between the two assets. We need this correlation because we are forecasting a VaR of the portfolio and evaluating if our predictions represent what actually happened.
*Jen-Jsung Huang, Kuo-Jung Lee, Hueimei Liang, Wei-Fu Lin, Estimating value at risk of portfolio by conditional copula-GARCH method, Insurance: Mathematics and Economics, Volume 45, Issue 3, 2009,