A distance test of normality for a wide class of stationary processes

A distance test for normality of the one-dimensional marginal distribution of stationary fractionally integrated processes is considered. The test is implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the test statistic. The bootstrap-based test does not require knowledge of either the dependence parameter of the data or of the appropriate norming factor for the test statistic. The small-sample properties of the test are examined by means of Monte Carlo experiments. An application to real-world data is also presented.