A Consistent Nonparametric Test for Causality

We propose a nonparametric test for Granger-type causality. A conceptually similar work will be Hidalgo (2000), who introduced a nonparametric Granger causality test in the frequency domain for weakly stationary linear processes. He is mainly concerned with the test under long range dependent observations, and it does not have a power against some alternatives of series with nonlinear dynamics. We construct a test statistic based on moment conditions allowing for nonlinear dependence. The test has a nontrivial power against T1/2-local alternatives where T is sample size. Its null asymptotic distribution is not normal, but we can easily calculate the critical region by simularion.