On Properties of the MixedTS Distribution and Its Multivariate Extension

Abstract

A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated. We discuss a random number generating procedure and introduce an estimation methodology based on the minimisation of a distance between empirical and theoretical characteristic functions. Asymptotic tail behaviour of the univariate Mixed Tempered Stable is exploited in the estimation procedure in order to obtain a better fitting on tails. Advantages of the multivariate Mixed Tempered Stable distribution are discussed and illustrated via numerical analysis.

Modeling Tail Risk with Tempered Stable Distributions: An Overview

“…The subordination approach has been studied from a univariate perspective by Hurst et al (1997) and Hurst et al (1999), and from a multivariate perspective by Guillaume (2013), Tassinari and Bianchi (2014), Fallahgoul et al (2016), Bianchi et al (2016), Fallahgoul et al (2018b, Hitaj et al (2018), and Bianchi and Tassinari (2018). In the present study, we do not discuss the tempered stable distribution in a multivariate context.…”

Locally stationary processes with stable and tempered stable innovations

“…There are different extensions or subclasses of tempered stable distribution, e.g. mixed tempered stable distribution (Hitaj et al, 2018;Rroji and Mercuri, 2015), modified tempered stable distribution (Kim et al, 2006) and KR distribution (Kim et al, 2008). Despite of these variations, we will focus on the standardized classical tempered stable distribution, which is implemented in GARCH models in Kim et al (2008).…”