On properties of the MixedTS distribution and its multivariate extension

A review of the univariate MixedTS is given and some new results on the asymptotic tail behavior are derived. The multivariate version of the Mixed Tempered Stable, which is a generalization 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 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 fitting on tails. Advantages of the multivariate Mixed Tempered Stable distribution are discussed and illustrated via numerical analysis.