Testing Distributional Granger Causality With Entropic Optimal Transport

ABSTRACT We develop a novel nonparametric test for Granger causality in distribution based on entropic optimal transport. Unlike classical mean‐based approaches, the proposed method directly compares the full conditional distributions of a response variable with and without the history of a candidate predictor. This allows for the detection of causal effects that arise from changes in dispersion, skewness, tail behavior, or multimodality. The test statistic is constructed as a temporal average of entropically regularized Wasserstein distances between kernel‐smoothed conditional distributions. We establish uniform consistency of the estimators, derive the non‐asymptotic exponential concentration bound, and prove a central limit theorem under weak temporal dependence. The test achieves the minimax optimal detection boundary over Hölder classes and remains robust to mild misspecification of the conditioning set. For valid inference in finite samples, we develop a stationary bootstrap procedure that preserves temporal dependence and consistently approximates the sampling distribution of the test statistic. Simulation studies demonstrate reliable size control and high power across a broad range of nonlinear and distributional data generating processes. An empirical application to financial volatility forecasting reveals dynamic causal patterns that are not detected by existing Granger causality tests.