A Deep Learning Test of the Martingale Difference Hypothesis

Abstract

A deep learning binary classifier is proposed to test if asset returns follow martingale difference sequences. The Neyman–Pearson classification paradigm is applied to control the type I error of the test. In Monte Carlo simulations, I find that this approach has better power properties than variance ratio and portmanteau tests against several alternative processes. I apply this procedure to a large set of exchange rate returns and find that it detects several potential deviations from the martingale difference hypothesis that the conventional statistical tests fail to capture.