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Conference Paper (international conference)

Elliptical Stable Distributions

Omelchenko Vadym

: Mathematical Methods in Economics 2010 , Eds: Houda Michal, Friebelova Jana

: Mathematical Methods in Economics 2010, (České Budějovice, CZ, 08.09.2010-10.09.2010)

: CEZ:AV0Z10750506

: GD402/09/H045, GA ČR

: Stable Distribution, Elliptical stable distributions, Maximum Likelihood Projections Estimators

: http://library.utia.cas.cz/separaty/2012/E/omelchenko-elliptical stable distributions.pdf

(eng): The elliptical stable distributions represent a symmetric subfamily of the stable distributions. Their advantage contrary to the general stable distributions consists in their easy-to-use property and the highest resemblance to the normal distribution. They enable an easy representation of the dependence structure of the margins by means of a matrix Q the same as in case of the normal distribution. In general, the dependence structure between margins is given in form of a spectral measure which can be even continuous. The computations and approximations require so much time that it just the fact that many practitioners avoid using general stable distributions. The general stable distributions possess so many additional properties that they barely take after the multivariate normal distribution. But the multi-variate elliptical stable distributions can be easily simulated and the estimation of their parameters can be obtained by methods whose preciseness is almost the same as the one of the maximum likelihood methodology.

: AH