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Barndorff-Nielsen, Ole Eiler and Stelzer, Robert (2004): Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy-Processes. Collaborative Research Center 386, Discussion Paper 381
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Abstract

Expressions for (absolute) moments of generalized hyperbolic (GH) and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centered at the location parameter mu explicit expressions as series containing Bessel functions are provided. Furthermore the derivatives of the logarithms of (absolute) mu-centered moments with respect to the logarithm of time are calculated explicitly for NIG Levy processes. Computer implementation of the formulae obtained is briefly discussed. Finally some further insight into the apparent scaling behaviour of NIG Levy processes (previously discussed in Barndorff-Nielsen and Prause (2001)) is gained.