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.

On Properties of the MixedTS Distribution and Its Multivariate Extension / A. Hitaj, F. Hubalek, L. Mercuri, E. Rroji. - In: INTERNATIONAL STATISTICAL REVIEW. - ISSN 0306-7734. - 86:3(2018 Dec), pp. 512-540. [10.1111/insr.12265]

On Properties of the MixedTS Distribution and Its Multivariate Extension

L. Mercuri
Penultimo
;
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.
MixedTS distribution; MixedTS Lévy process; MixedTS tails; Multivariate MixedTS
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
dic-2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/571641
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