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