In this paper we introduce an efficient fat-tail measurement framework that is based on  conditional second moments. We construct  goodness-of-fit statistic that has a direct financial interpretation and can be used to assess the impact of fat-tails on central data normality assumption . Next, we show how to use our framework to construct a powerful statistical normality test. In particular, we compare our methodology to various popular normality statistical tests, including the Jarque--Bera test that is based on third and fourth moments, and show that in most considered 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.
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.
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the
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financial
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normality assumption
conditional dispersion
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our
this
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statistical
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statistical
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most considered
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market-stock
market stock