Abstract
Bayesian Model Selection of Regular Vine Copulas
Highlights
Multivariate models do not typically allow much customization of either marginal or dependence characteristics
We propose sparsity-inducing but otherwise non-informative priors and provide a fully Bayesian extension of Gruber and Czado (2015)’s Bayesian tree-by-tree method that estimates all levels of a regular vine copula jointly
We present a method to estimate the posterior distribution of all levels of a regular vine copula jointly—the output are many different regular vine copulas that represent draws from the posterior distribution of all regular vine copulas
Summary
Multivariate models do not typically allow much customization of either marginal or dependence characteristics. A copula is a multivariate distribution function C with uniform marginals. It forms a multivariate distribution F1:d out of the univariate marginal distributions F1, . There is a rich set of bivariate copulas available of which the theoretical properties are known and the densities are analytically tractable (Joe, 2001). This motivates the pair copula construction: combine a number of different bivariate—“pair”—copulas using nested conditioning to create a multivariate copula (Joe, 1996; Bedford and Cooke, 2001)
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