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april 2006 Skewed Normal Variance-Mean Models for Asset Pricing and the Method of Moments
Annelies Tjetjep, Eugene Seneta
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Internat. Statist. Rev. 74(1): 109-126 (april 2006).


Financial returns (log-increments) data, Yt, t=1,2,..., are treated as a stationary process, with the common distribution at each time point being not necessarily symmetric.

We consider as possible models for the common distribution four instances of the General Normal Variance-Mean Model (GNVM), which is described by Y |VN(a(b+V),c 2 V+d 2) where V is a non-negative random variable and a, b, c and d are constants. When V is Gamma distributed and d=0, Y has the skewed Variance-Gamma distribution (VG). When V follows a Half Normal distribution and c=0, Y has the well-known Skew Normal (SN) distribution. We also consider two cases where V is Exponentially distributed. Bounds for skewness and kurtosis in each case are found in terms of the moments of the V. These are useful in determining whether the Method of Moments for a given model is feasible. The problem of overdetermination of parameters via estimating equations is examined. 5 data sets of actual returns data, chosen because of their earlier occurrence in the literature, are analysed using each of the 4 models.


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Annelies Tjetjep. Eugene Seneta. "Skewed Normal Variance-Mean Models for Asset Pricing and the Method of Moments." Internat. Statist. Rev. 74 (1) 109 - 126, april 2006.


Published: april 2006
First available in Project Euclid: 29 March 2006

zbMATH: 1131.62096

Keywords: exponential distribution , Laplace distribution , method of moments , Normal Variance-Mean distribution , Skewed Normal , Skewness, Kurtosis , Variance-Gamma distribution

Rights: Copyright © 2006 International Statistical Institute


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Vol.74 • No. 1 • april 2006
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