Some Properties of the Multivariate Generalized Hyperbolic Laws

Stergios B. Fotopoulos (), Venkata K. Jandhyala and Alex Paparas
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Stergios B. Fotopoulos: Washington State University
Venkata K. Jandhyala: Washington State University
Alex Paparas: Washington State University

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 8, 187-205

Abstract: 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.

Keywords: Scale mixture of multivariate distributions; Generalized inverse Gaussian distributions; Non Gaussian; Conditional laws.; Primary 60E10; 60E07; Secondary 62H05; 60G15; 60F05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-019-00173-4

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