A Simple Out-of-Sample Test for the Martingale Difference Hypothesis

Pablo Pincheira

Working Papers Central Bank of Chile from Central Bank of Chile

Abstract: We show that a straightforward modification of a trading based test for predictability displays interesting advantages over the Excess Profitability (EP) test proposed by Anatolyev and Gerco when testing the Martingale Difference Hypothesis. Our statistic is called Straightforward Excess Profitability (SEP) and avoids the calculation of a term that under the null of no predictability should be zero, but in practice may be sizable. In addition, our test does not require the strong assumption of independency used to derive the EP test. We claim that dependency is the rule and not the exception. We show via Monte Carlo simulations that the SEP test outperforms the EP test in terms of size and power. Finally, we illustrate the use of these tests in an empirical application within the context of the exchange rate literature.

Date: 2013-07
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