Bayesian Model Choice of Grouped t-copula

TL;DR

This paper introduces a Bayesian MCMC approach for selecting among t-copula models, including a generalized grouped t-copula, using FX rate data, and demonstrates its impact on risk assessment.

Contribution

It develops a Bayesian inference framework for model selection of generalized grouped t-copulas, enhancing flexibility and accuracy in dependence modeling.

Findings

Bayesian criteria favor the generalized t-copula over other models.

Model choice influences the estimated conditional Value-at-Risk.

Results align with classical likelihood ratio tests.

Abstract

One of the most popular copulas for modeling dependence structures is t-copula. Recently the grouped t-copula was generalized to allow each group to have one member only, so that a priori grouping is not required and the dependence modeling is more flexible. This paper describes a Markov chain Monte Carlo (MCMC) method under the Bayesian inference framework for estimating and choosing t-copula models. Using historical data of foreign exchange (FX) rates as a case study, we found that Bayesian model choice criteria overwhelmingly favor the generalized t-copula. In addition, all the criteria also agree on the second most likely model and these inferences are all consistent with classical likelihood ratio tests. Finally, we demonstrate the impact of model choice on the conditional Value-at-Risk for portfolios of six major FX rates.