Bayesian model selection for hierarchical copulas and vines

Copula models provide an effective tool for modeling joint distributions. Model selection allowing to choose an appropriate subclass of copulas remains a critical issue for many applications. The paper suggests an implementation of Bayesian model selection procedure based on ideas of Bretthorst, Huard et al. It allows us to compare several classes of Archimedean copulas (Frank’s, Clayton’s, and and survival Gumbel-Hougaard families) and elliptical copulas (Gaussian and Student t-copulas). For dimensions higher than 2 we consider several types of hierarchical structures including nested Archimedean copulas, hierarchical Kendall copulas and vines. We consider a portfolio based on four national indices. Extreme market co-movements are modeled by the tail behavior of the joint distribution or index returns and currency exchange rates. Estimation of parameters within suggested copula families and hierarchical structures is carried out via empirical Bayes approach using random walk Metropolis algorithm and other Markov chain Monte Carlo techniques