Bayesian Mixture Copula Estimation and Selection with Applications

Mixture copulas are popular and essential tools for studying complex dependencies among variables. However, selecting the correct mixture models often involves repeated testing and estimations using criteria such as AIC, which could require effort and time. In this paper, we propose a method that would enable us to select and estimate the correct mixture copulas simultaneously. This is accomplished by first overfitting the model and then conducting the Bayesian estimations. We verify the correctness of our approach by numerical simulations. Finally, the real data analysis is performed by studying the dependencies among three major financial markets.