Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Rafał Weron ()

Econometrics from EconWPA

Abstract: Power-law tail behavior and the summation scheme of Levy-stable (alpha- stable) distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0 < alpha < = 2 ). In this paper we illustrate that widely used tail index estimates (log-log linear regression and Hill) can give exponents well above the asymptotic limit for alpha close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent alpha around 3 may very well indicate a Levy-stable distribution with alpha around 1.8.

Keywords: Levy-stable distribution; Alpha-stable distribution; Tail exponent; Hill estimator (search for similar items in EconPapers)
JEL-codes: C13 C50 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets
Date: 2003-05-16
Note: Type of Document - PDF; prepared on PC-TEX; pages: 14 ; figures: 10 included. Appeared in: International Journal of Modern Physics C, Vol. 12, No. 2 (2001) 209-223.
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpem:0305003

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