Abstract: Generalized Hyperbolic Distribution (GHD) arises as a normal variance-mean mixture with Generalized Inverse Gaussian (GIG) as the mixing distribution. The GHD nests a number of distributions obtained as special and limiting cases. In literature, however, Normal Inverse Gaussian (NIG) and Variance-Gamma (VG) are the most commonly used special and limiting cases, respectively, in analyzing financial data. The objective of this paper is to derive another special case of the GHD, obtain its properties, estimate its parameters and then apply it to some financial data. The properties are determined by first expressing them in terms of the corresponding properties of the mixing distribution. The maximum likelihood estimates are obtained using the Expectation-Maximization (EM) algorithm which overcomes numerical difficulties occurring when standard numerical techniques are used. An application to a dataset concerning the Range Resource Corporation (RRC) is given. It is shown that the proposed model captures the skewness and excess kurtosis exhibited by the data. The maximum likelihood estimates are shown to be obtained easily by the EM-algorithm. |
Keywords and phrases: modified Bessel function of the third kind, generalized inverse Gaussian distribution, generalized hyperbolic distribution, EM-algorithm.
Received: March 17, 2021; Revised: April 22, 2021; Accepted: October 10, 2021; Published: November 16, 2021
How to cite this article: Calvin B. Maina, Patrick G. O. Weke, Carolyne A. Ogutu and Joseph A. M. Ottieno, Properties, estimation and application to financial data for generalized hyperbolic distribution when the index parameter is , Advances and Applications in Statistics 71(1) (2021), 55-84. DOI: 10.17654/AS071010055
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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