This article examines testing the Martingale Difference Hypothesis (MDH) follow a martingale, it is more common to test that returns follow a. A Martingale Test for 'Alpha'. Dean P. Foster*, Robert Stine*, H. Peyton Young**. This version: January 31, *Department of Statistics, Wharton School. This paper proposes a statistical test of the martingale hypothesis. It can be used to test whether a given time series is a martingale process against certain.