Multivariate Skew Distributions Based on the GT-Copula

Abstract

In this paper we obtain the expression for the copula pertaining to the multivariate generalized t distribution, the generalized t-copula, or in short, GT-copula. The GT-copula generalizes some well known copulas, such as the one associated with the multivariate t distribution (t-copula). We derive the expression for its tail dependence coefficient and show that the GT-copula may adjust for stronger tail dependence when compared to the t-copula. The potentiality of the GT-copula allows for modeling varying degrees and different types (linear and nonlinear) of dependence, as well as multimodality. By applying Sklar’s theorem to the GT-copula, and by mixing symmetric and asymmetric margins, we construct a new family of multivariate distributions. The resulting distributions are suitable for modeling a wide variety of skew datasets. The flexibility of the copula approach suggests applications in many fields, such as environment and finance. We provide an illustration, where we quantify stock market linkages.