Normality tests for dependent data: large-sample and bootstrap approaches

Abstract

The paper considers the problem of testing for normality of the one-dimensional marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using an autoregressive sieve bootstrap procedure to obtain critical values and P-values for normality tests is explored. The small-sample properties of a variety of tests are investigated in an extensive set of Monte Carlo experiments. The bootstrap version of the classical skewness–kurtosis test is shown to have the best overall performance in small samples.

Keywords:

• Autoregressive sieve Bootstrap
• Normality test
• Weak dependence

Acknowledgments

We wish to thank an anonymous referee for helpful comments. We are also grateful to Antonio Trujillo-Ortiz for making some of his Matlab code available.