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On Properties of the MixedTS Distribution and Its Multivariate Extension

Author

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  • Asmerilda Hitaj
  • Friedrich Hubalek
  • Lorenzo Mercuri
  • Edit Rroji

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.

Suggested Citation

  • Asmerilda Hitaj & Friedrich Hubalek & Lorenzo Mercuri & Edit Rroji, 2018. "On Properties of the MixedTS Distribution and Its Multivariate Extension," International Statistical Review, International Statistical Institute, vol. 86(3), pages 512-540, December.
    • Handle: RePEc:bla:istatr:v:86:y:2018:i:3:p:512-540
    DOI: 10.1111/insr.12265
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    Cited by:

    1. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.

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