Tractable Unified Skew-t Distribution and Copula for Heterogeneous Asymmetries

TL;DR

This paper introduces a new tractable variant of the Unified Skew-t distribution and its copula, enabling more flexible modeling of asymmetric heavy-tailed data with improved computational feasibility.

Contribution

A novel TrUST distribution and copula are proposed, addressing parameter identification and computational challenges of existing models, with demonstrated practical advantages.

Findings

Enhanced modeling of asymmetric heavy-tailed data.

Bayesian inference methods for the TrUST distribution and copula.

Improved accuracy over existing skew-t models in real data applications.

Abstract

Multivariate distributions that allow for asymmetry and heavy tails are important building blocks in many econometric and statistical models. The Unified Skew-t (UST) is a promising choice because it is both scalable and allows for a high level of flexibility in the asymmetry in the distribution. However, it suffers from parameter identification and computational hurdles that have to date inhibited its use for modeling data. In this paper we propose a new tractable variant of the unified skew-t (TrUST) distribution that addresses both challenges. Moreover, the copula of this distribution is shown to also be tractable, while allowing for greater heterogeneity in asymmetric dependence over variable pairs than the popular skew-t copula. We show how Bayesian posterior inference for both the distribution and its copula can be computed using an extended likelihood derived from a generative representation of the distribution. The efficacy of this Bayesian method, and the enhanced flexibility of both the TrUST distribution and its implicit copula, is first demonstrated using simulated data. Applications of the TrUST distribution to highly skewed regional Australian electricity prices, and the TrUST copula to intraday U.S. equity returns, demonstrate how our proposed distribution and its copula can provide substantial increases in accuracy over the popular skew-t and its copula in practice.