Before revision:  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.
After revision:  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 conditional dispersion . Next, we show how to use our framework to construct a powerful statistical normality test.