Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

26 Pages Posted: 6 Apr 2010 Last revised: 14 Apr 2010

See all articles by Matteo Bonato

Matteo Bonato

University of Johannesburg - Department of Economics and Econometrics; Valdon Group GhmB

Date Written: April 1, 2010

Abstract

This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. I first show that for symmetric fat tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, I study, via Monte Carlo simulations, the behavior of the alternative measures of skewness and kurtosis when applied to distributions that do not possess finite higher moments. Finally, I present an application to the series of daily returns on a large cap US stock and show why alternative measures are a better tool to describe the distribution of financial returns.

Keywords: Skewness, Kurtosis, Fat Tails, Outliers

JEL Classification: C10, C15, C16

Suggested Citation

Bonato, Matteo, Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments (April 1, 2010). Available at SSRN: https://ssrn.com/abstract=1582854 or http://dx.doi.org/10.2139/ssrn.1582854

Matteo Bonato (Contact Author)

University of Johannesburg - Department of Economics and Econometrics ( email )

P.O. Box 524
Auckland Park 2006, Johannesburg
South Africa

Valdon Group GhmB ( email )

Zurich
Germany

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