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.

Hitaj, A., Hubalek, F., Mercuri, L., Rroji, E. (2018). On Properties of the MixedTS Distribution and Its Multivariate Extension. INTERNATIONAL STATISTICAL REVIEW, 86(3), 512-540 [10.1111/insr.12265].

On Properties of the MixedTS Distribution and Its Multivariate Extension

Hitaj, Asmerilda
;
Mercuri, Lorenzo;Rroji, Edit
2018

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.
Articolo in rivista - Articolo scientifico
MixedTS distribution; MixedTS Lévy process; MixedTS tails; multivariate MixedTS;
MixedTS distribution; MixedTS Lévy process; MixedTS tails; Multivariate MixedTS; Statistics and Probability; Statistics, Probability and Uncertainty
English
512
540
29
Hitaj, A., Hubalek, F., Mercuri, L., Rroji, E. (2018). On Properties of the MixedTS Distribution and Its Multivariate Extension. INTERNATIONAL STATISTICAL REVIEW, 86(3), 512-540 [10.1111/insr.12265].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/197021
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