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Some Properties of the Multivariate Generalized Hyperbolic Laws

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Abstract

The purpose of this study is to characterize multivariate generalized hyperbolic (MGH) distributions and their conditionals by considering the MGH as a subclass of the mean-variance mixing of the multivariate normal law. The essential contribution here lies in expressing MGH densities by utilizing various integral representations of the Bessel function. Moreover, in a more convenient form these modified density representations are more advantageous for deriving limiting results. The forms are also convenient for studying the transient as well as tail behavior of MGH distributions. The results include the normal distribution as a limiting form for the MGH distribution. To support the MGH model an empirical study is conducted to demonstrate the applicability of the MGH distribution for modeling not only high frequency data but also for modeling low frequency data. This is against the currently prevailing notion that the MGH model is relevant for modeling only high frequency data.

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Authors and Affiliations

  1. Department of Finance and Management Science, Washington State University, Pullman, WA, 99164-4746, USA

    Stergios B. Fotopoulos & Alex Paparas

  2. Department of Mathematics & Statistics, Washington State University, Pullman, WA, 99164-4113, USA

    Venkata K. Jandhyala

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  1. Stergios B. Fotopoulos
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  2. Venkata K. Jandhyala
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  3. Alex Paparas
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Correspondence to Stergios B. Fotopoulos.

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Fotopoulos, S.B., Jandhyala, V.K. & Paparas, A. Some Properties of the Multivariate Generalized Hyperbolic Laws. Sankhya A 83, 187–205 (2021). https://doi.org/10.1007/s13171-019-00173-4

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