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

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.