A consistent nonparametric test for serial independence

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 χ12, 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.