A Deep Learning Test of the Martingale Difference Hypothesis

João Bastos

Journal of Forecasting, 2025, vol. 44, issue 6, 1993-2001

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.

Date: 2025
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https://doi.org/10.1002/for.3280

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Working Paper: A deep learning test of the martingale difference hypothesis (2025)
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