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Duality between matrix variate and matrix variate V.G. distributions
- Source :
-
Journal of Multivariate Analysis . Jul2006, Vol. 97 Issue 6, p1467-1475. 9p. - Publication Year :
- 2006
-
Abstract
- Abstract: The (univariate) -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 -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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0047259X
- Volume :
- 97
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Multivariate Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 20900868
- Full Text :
- https://doi.org/10.1016/j.jmva.2005.09.002