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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, the authors 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.
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