A nonparametric test of serial independence based on the empirical distribution function

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests of serial dependence. An extension of the test is made to detect higher lag dependence, and finally the test is applied to a real data example.