Time-varying copulas on equity

I apply constant and time-varying parameter variants of the normal and Symmetrized Joe-Clayton copula to AR(p)-GARCH(1,1) models of the DAX - FTSE100, S&P500 - FTSE100 and the S&P - S&P/TSX returns of equity price indices. Using a likelihood ratio test, I find that time-varying copulas provide a signicantly better model t than copulas with constant parameters. The North-American dependence seems to be more volatile on the short term and the European dependence seems to have a structural break around 2005. The VaR models for the 99% VaR seem to perform well, but the 95% and 90% VaR slightly overestimate the risk. Timevarying copula VaR models don't perform better than constant copula VaR models, but it does outperform the benchmark model.