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Robust estimation of skewness and kurtosis in distributions with infinite higher moments

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  • Bonato, Matteo

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. It is first shown that for symmetric fat-tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, a Monte Carlo simulation is performed to investigate the behavior of the alternative measures of skewness and kurtosis when applied to distributions which do not possess finite higher moments. Finally, an application to the series of daily returns on a large cap US stock is presented to explain why alternative measures are a better tool to describe the distribution of financial returns.

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  • Bonato, Matteo, 2011. "Robust estimation of skewness and kurtosis in distributions with infinite higher moments," Finance Research Letters, Elsevier, vol. 8(2), pages 77-87, June.
    • Handle: RePEc:eee:finlet:v:8:y:2011:i:2:p:77-87
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    Cited by:

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    3. Dangxing Chen, 2019. "Does the leverage effect affect the return distribution?," Papers 1909.08662, arXiv.org, revised Sep 2019.
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    7. Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
    8. Barrera, Carlos, 2022. "Characterizing the Anchoring Effects of Official Forecasts on Private Expectations," MPRA Paper 114258, University Library of Munich, Germany.
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