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 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 fi...

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Bibliographic Details
Published in:International statistical review 2018-12, Vol.86 (3), p.512-540
Main Authors: Hitaj, Asmerilda, Hubalek, Friedrich, Mercuri, Lorenzo, Rroji, Edit
Format: Article
Language:English
Subjects:
Asymptotic properties
Characteristic functions
Dependence
Empirical analysis
MixedTS distribution
MixedTS Lévy process
MixedTS tails
multivariate MixedTS
Numerical analysis
Random numbers
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Summary: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.
ISSN:0306-7734
1751-5823
DOI:10.1111/insr.12265