Duality between matrix variate t and matrix variate V.G. distributions

Solomon W. Harrar, Eugene Seneta and Arjun K. Gupta

Journal of Multivariate Analysis, 2006, vol. 97, issue 6, 1467-1475

Abstract: The (univariate) t-distribution and symmetric V.G. distribution are competing models [D.S. Madan, E. Seneta, The variance gamma (V.G.) model for share market returns, J. Business 63 (1990) 511-524; T.W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2000 (Section 9.4)] for the distribution of log-increments of the price of a financial asset. Both result from scale-mixing of the normal distribution. The analogous matrix variate distributions and their characteristic functions are derived in the sequel and are dual to each other in the sense of a simple Duality Theorem. This theorem can thus be used to yield the derivation of the characteristic function of the t-distribution and is the essence of the idea used by Dreier and Kotz [A note on the characteristic function of the t-distribution, Statist. Probab. Lett. 57 (2002) 221-224]. The present paper generalizes the univariate ideas in Section 6 of Seneta [Fitting the variance-gamma (VG) model to financial data, stochastic methods and their applications, Papers in Honour of Chris Heyde, Applied Probability Trust, Sheffield, J. Appl. Probab. (Special Volume) 41A (2004) 177-187] to the general matrix generalized inverse gaussian (MGIG) distribution.

Keywords: Characteristic; function; Inversion; theorem; Inverted; Wishart; Log; return; Matrix; generalized; inverse; Gaussian; Matrix; variate; distributions; Wishart; Variance-gamma (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (3)

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