Bayesian Inference for Multivariate Copulas Using Pair-Copula Constructions

Abstract

We provide a Bayesian analysis of pair-copula constructions (PCCs) (Aas et al., 2009), which outperform many other multivariate copula constructions in modeling dependencies in financial data. We use bivariate t-copulas as building blocks in a PCC to allow extreme events in bivariate margins individually. While parameters may be estimated by maximum likelihood, confidence intervals are difficult to obtain. Consequently, we develop a Markov chain Monte Carlo (MCMC) algorithm and compute credible intervals. Standard errors obtained from MCMC output are compared to those obtained from a numerical Hessian matrix and bootstrapping. As applications, we consider Norwegian financial returns and Euro swap rates. Finally, we apply the Bayesian model selection approach of Congdon (2006) to identify conditional independence, thus constructing more parsimonious PCCs.