Testing the Martingale Hypothesis
We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramér-von Mises tests. The tests are distribution free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The paper develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, non-martingale processes. Simulations show that the tests have good ﬁnite sample properties in comparison with other tests particularly under conditional heteroskedasticity and mildly explosive alternatives. An empirical application to major exchange rate data ﬁnds strong evidence in favor of the martingale hypothesis, conﬁrming much earlier research.
Phillips, Peter C.B. and Jin, Sainan, "Testing the Martingale Hypothesis" (2013). Cowles Foundation Discussion Papers. 2300.