Rank Tests for Serial Dependence

Abstract.A family of linear rank statistics is proposed in order to test the independence of a time series, under the assumption that the random variables involved have symmetric distributions with zero medians, without the standard assumptions of normality or identical distributions. The family considered includes analogues of the sign. Wilcoxon signed‐rank and van der Waerden tests for symmetry about zero and tables constructed for these tests remain applicable in the present context. The tests proposed are exact and may be applied to assess serial dependence at lag one or greater. The procedures developed are illustrated by a test of the efficiency of forward exhange rates as predictors of future spot rates during the German hyperinflation.