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

Damian Jelito () and Marcin Pitera ()
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Damian Jelito: Jagiellonian University
Marcin Pitera: Jagiellonian University

Statistical Papers, 2021, vol. 62, issue 5, No 2, 2083-2108

Abstract: 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.

Keywords: 20-60-20 rule; Normality test; Fat-tail; Heavy-tail; Non-normality; Stock returns; 62F03; 62F05; 62P05; 62P20; 91G70 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01176-2

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DOI: 10.1007/s00362-020-01176-2

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