A consistent nonparametric test for serial independence

Abstract

We propose a nonparametric test for serial independence against serial dependence of fixed order that is consistent against all such alternatives. The conditions required are weak, the asymptotic distribution under the null is χ 1 2, and the test works regardless of the underlying distribution. Also included are a nuisance parameter result, Monte Carlo simulations, a theoretical efficiency study, an empirical example, and a review of possible extensions. In addition, we derive a similar consistent test for lack of serial dependence of order one against serial dependence of order one.