Self-normalized tests for skewness, kurtosis, and normality for time series data 

Abstract

Testing for skewness, kurtosis, and normality for time series data is highly relevant for modeling and testing purposes in econometrics. It also affects our understanding of many economic and financial phenomena and the validity of the models developed to explain them. In this paper, we propose self-normalized tests for skewness, kurtosis, and normality that can eliminate the effect of the long-run variance. In particular, our tests allow us to avoid using the long-run variance estimator, which is poorly approximated in finite samples. Consequently, our tests rule out the need to choose the lag-truncation parameter. We present general conditions on the self-normalization function and give two simple examples using the fixed-b asymptotics and the simple normalization proposed by Lobato (2001). Monte Carlo simulations show that the self-normalized tests for skewness and normality have good finite-sample size and power properties, while the test for kurtosis presents substantial size distortions unless the distribution has thin tails like the normal distribution. Finally, we apply the tests to 18 macroeconomic and financial series to study their symmetry, kurtosis, and normality. 

Keywords: Skewness, Kutosis, Normality Testing, Self-Normalization