Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy-Processes
Beschreibung
vor 20 Jahren
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.
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.
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