Multivariate Mixed Tempered Stable Distribution

TL;DR

This paper introduces a multivariate Mixed Tempered Stable distribution that generalizes Normal Variance Mean Mixtures, capable of modeling tail behavior and dependence structures, with applications demonstrated through simulations.

Contribution

It proposes the first multivariate version of the Mixed Tempered Stable distribution, including its properties, sampling method, and estimation procedure.

Findings

Effective in fitting tail behavior

Captures dependence between components

Demonstrated via simulation studies

Abstract

The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure between components are investigated. We discuss a random number generating procedure and introduce an estimation methodology based on the minimization of a distance between empirical and theoretical characteristic functions. Asymptotic tail behavior of the univariate Mixed Tempered Stable is exploited in the estimation procedure in order to obtain a better model fitting. Advantages of the multivariate Mixed Tempered Stable distribution are discussed and illustrated via simulation study.