A Nonparametric Test of Serial Independence Based on the Empirical Distribution Function
研究了Blum-Kiefer-Rosenblatt统计量在时间序列中检验序列独立性的表现，证明了其对一阶滞后相依备择假设的一致性，并给出了连续和离散边际分布下的零分布，通过模拟和实际数据验证了检验的效能。
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.