# Forecasting using Copula GARCH methods

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.

Thanks

*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,

• Please include a full reference to Huang et al. (2009). Consider describing the setup in more detail so that one is not required to read Huang et al. (2009) to be able to help you. This way you can increase your chances of getting a useful answer and decrease the chances of the question being closed as "unclear". Apr 16, 2022 at 10:47
• VAR is vector autoregression. VaR is value at risk. Var is variance. You wrote VAR, but I guess you meant VaR. Apr 18, 2022 at 19:17

Correlation will not help determine value at risk (VaR) from a nontrivial copula. The easiest and most general way to obtain VaR would be to

• simulate a large number (say, 10000) of future paths of the stock returns from the model,
• construct paths of portfolio returns corresponding to the given portfolio weights (0.5 and 0.5 in your case) and then
• estimate the VaR nonparametrically, i.e. obtain the appropriate empirical quantile of the simulated distribution.