In this paper we define a family of tests for the Martingale Difference Hypothesis (MDH) based upon a shrinkage principle. Tests within this family are such that rejection of the null implies that forecasts from the alternative model, adjusted by a shrinkage factor, will display lower Mean...

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...