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

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Summary

Introduction

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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