Multivariate dynamic Copula models : parameter estimation and forecast evaluation

This paper examines the time-varying dependence structure of commodity futures portfolios based on multivariate dynamic copula models. The importance of accounting for time-variation is emphasized in the context of the Basel traffic light system. We enhance the exibility of this structure by modeling regimes with multivariate mixture copulas and by applying the dynamic conditional correlation model (DCC) to multivariate elliptical copulas. The most suitable dynamic dependence model in terms of in-sample and out-of sample valuation is the dynamic Student-t-Clayton mixture copula, followed by the dynamic Student-t copula, and the dynamic Gaussian-Clayton mixture. In comparison to the multivariate normal model, the dynamic Clayton copula also scales down significantly the number of VAR(99%) violations during the 2007/08 financial crisis period. The predictive performance of our multivariate dynamic copula models confirms its superiority over bivariate regime-switching copula models for various states of the economy