Wilcoxon-Signed Rank Test for Long Memory Sequences

Abstract

The Wilcoxon-signed rank test and the sign test are studied under the hypothesis that data exhibit strong dependence features. Using nonlinear transformations of strongly dependent Gaussian sequences, a general setting, which covers most situations of interest, is analyzed. The asymptotic distributions of the tests are derived under fairly general conditions. Comparisons are made with corresponding results in the weakdependence case.