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An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions

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  • J. Martin van Zyl

Abstract

Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to heavy-tailed data where the 4th moment does not exist. The study will focus on samples from the symmetric stable distributions. It was found that the expected value of excess kurtosis divided by the sample size is finite for any value of the tail index and the sample estimate of kurtosis increases as a linear function of sample size and tail index. It is very sensitive to changes in the tail-index.

Suggested Citation

  • J. Martin van Zyl, 2018. "An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions," Papers 1811.00476, arXiv.org, revised Nov 2018.
    • Handle: RePEc:arx:papers:1811.00476
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    References listed on IDEAS

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    1. Anna M. Fiori & Michele Zenga, 2009. "Karl Pearson and the Origin of Kurtosis," International Statistical Review, International Statistical Institute, vol. 77(1), pages 40-50, April.
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    3. Nicholas J. Cox, 2010. "Speaking Stata: The limits of sample skewness and kurtosis," Stata Journal, StataCorp LP, vol. 10(3), pages 482-495, September.
    4. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
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