Bayesian Inference in Multivariate Stable Distributions Using Copulae

Abstract

In this paper we take up Bayesian inference in multivariate stable distributions through innovative multivariate stable copulae. The problem that the characteristic function is defined through a difficult object, the spectral measure is completely bypassed by our approach. The new methods are applied to major exchange rates with encouraging results. The copula-based technique is based on non-parametric margins (both data-estimated as well as Dirichlet process priors) and we compare with a multivariate stable copula whose margins can be normal, Student-t or univariate stable.