Bayesian inference for D-vine pair-copula constructions: Estimation and model selection

Copulas are nowadays a standard tool for stochastic modeling in different fields of applied science. Therefore the construction of flexible multivariate copulas and the choice of the best fitting copula model are extremely important statistical issues. Recently empirical studies find regular vine pair-copula constructions (PCC) the most successful in fitting financial time series. In this talk we restrict ourselves to a particular class of regular vines called D-vine and discuss a Bayesian analysis for D-vine PCCs. First we develop an estimation procedure for D-vine PCCs based on bivariate t-copulas in a Bayesian framework. However the methodology is general and can easily be extended to all known bivariate copula families. Then we approach in two different ways the selection problem of finding the most parsimonious D-vine PCC model by capturing (conditional) independencies. In the first approach we derive and implement a reversible jump Markov chain Monte Carlo (MCMC) algorithm while the second approach utilizes indicator variables in a MCMC framework. Both approaches solve model selection and estimation problems for D-vine PCCs simultaneously. The talk is based on joint work with Carlos Almeida, Claudia Czado and Michael Smith.