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.

在本文中，我们介绍了一种基于条件二阶矩的高效肥尾测量框架。我们构建了一个具有直接解释的拟合优度统计量，可用于评估肥尾对中心数据条件分散的影响。接下来，我们将展示如何使用这个框架来构建一个强大的正态性测试。特别是，我们将我们的方法与各种流行的正态性检验进行了比较，包括基于三次和四次矩的 Jarque-Bera 检验，并表明在许多情况下，我们的框架在模拟和市场股票数据上都优于所有其他框架。最后，我们推导出条件均值和方差估计量的渐近分布，并使用它来显示所提出的检验统计量的渐近正态性。