An out-of-sample, nonparametric test of the martingale difference hypothesis

In this paper I provide analytical, simulation, and empirical evidence rega rding a simple test used to determine whether a scalar variable Oil forms a martingale difference sequence (m.d.s.). The test is based upon an asympto tically valid upper bound on the difference between out-of-sample MSE's cal culated once under the null and then once under the alternative using a ker nel-based estimate of the conditional mean. The test considered here differ s from other proposed tests by (1) estimating the conditional mean under th e alternative using the kernel-based Nadarya-Watson estimator, and (2) focu sing exclusively on ex-ante rather than ex-post predictive ability. Simulat ion evidence regarding the test indicates reasonable power characteristics though often at the expense of large size distortions. An application of th e test to predictions of excess returns to the S&P 500 composite portfolio generally indicates little predictive ability during the 1970s and 1980s. T he test does indicate some predictive ability during the 1990s.