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New fat-tail normality test based on conditional second moments with applications to finance

Author

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  • Damian Jelito

    (Jagiellonian University)

  • Marcin Pitera

    (Jagiellonian University)

Abstract

In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framework to construct a powerful normality test. In particular, we compare our methodology to various popular normality tests, including the Jarque–Bera test that is based on third and fourth moments, and show that in many cases our framework outperforms all others, both on simulated and market stock data. Finally, we derive asymptotic distributions for conditional mean and variance estimators, and use this to show asymptotic normality of the proposed test statistic.

Suggested Citation

  • Damian Jelito & Marcin Pitera, 2021. "New fat-tail normality test based on conditional second moments with applications to finance," Statistical Papers, Springer, vol. 62(5), pages 2083-2108, October.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01176-2
    DOI: 10.1007/s00362-020-01176-2
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    References listed on IDEAS

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    1. Thorsten Thadewald & Herbert Buning, 2007. "Jarque-Bera Test and its Competitors for Testing Normality - A Power Comparison," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 87-105.
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    5. Piotr Jaworski & Marcin Pitera, 2017. "A note on conditional covariance matrices for elliptical distributions," Papers 1703.00918, arXiv.org.
    6. Jaworski, Piotr & Pitera, Marcin, 2017. "A note on conditional covariance matrices for elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 230-235.
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    8. A. Desgagné & P. Lafaye de Micheaux, 2018. "A powerful and interpretable alternative to the Jarque–Bera test of normality based on 2nd-power skewness and kurtosis, using the Rao's score test on the APD family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(13), pages 2307-2327, October.
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    Cited by:

    1. Jacobovic, Royi & Kella, Offer, 2022. "A characterization of normality via convex likelihood ratios," Statistics & Probability Letters, Elsevier, vol. 186(C).

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