Trending Mixture Copula Models with Copula Selection

Modeling the joint tails of multiple nancial time series has important implications for risk management. Classical models for dependence often encounter a lack of t in the joint tails, calling for additional exibility. In this paper we introduce a new nonparametric time-varying mixture copula model, in which both weights and dependence parameters are deterministic functions of time. We propose penalized trending mixture copula models with group smoothly clipped absolute deviation (SCAD) penalty functions to do the estimation and copula selection simultaneously. Monte Carlo simulation results suggest that the shrinkage estimation procedure performs well in selecting and estimating both constant and trending mixture copula models. Using the proposed model and method, we analyze the evolution of the dependence among four international stock markets, and nd substantial changes in the levels and patterns of the dependence, in particular around crisis periods.