Deep learning based doubly robust test for Granger causality

2025-09-19

AI Summary

To address the curse of dimensionality plaguing conventional nonlinear Granger causality tests under high-dimensional lag orders, this paper proposes a deep learning–based doubly robust testing framework. The method constructs a neural network–driven doubly robust test statistic achieving parametric convergence rates and employs the multiplier bootstrap for efficient critical value calibration—bypassing computationally prohibitive high-dimensional kernel estimation and grid search. Theoretically, the test asymptotically controls Type I error and attains full power. Extensive numerical simulations demonstrate its superior finite-sample performance in high-lag, low-sample-size settings. Empirically, the method successfully re-examines nonlinear causal directions among stock prices and trading volumes across China, the U.S., and Japan. By integrating deep learning with semiparametric efficiency theory, this work advances econometrics toward a new paradigm of high-dimensional, nonparametric, and interpretable causal inference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Granger causality is popular for analyzing time series data in many applications from natural science to social science including genomics, neuroscience, economics, and finance. Consequently, the Granger causality test has become one of the main concerns of the econometrician for decades. Taking advantage of the theoretical breakthroughs in deep learning in recent years, we propose a doubly robust Granger causality test (DRGCT). Our method offers several key advantages. The first and most direct benefit is for the users, DRGCT allows them to handle large lag orders while alleviating the curse of dimensionality that traditional nonlinear Granger causality tests usually face. Second, introducing a doubly robust test statistic for time series based on neural networks that achieves a parametric convergence rate not only suggests a new paradigm for nonparametric inference in econometrics, but also broadens the application scope of deep learning. Third, a multiplier bootstrap method, combined with the doubly robust approach, provides an efficient way to obtain critical values, effectively reducing computational time and avoiding redundant calculations. We prove that the test asymptotically controls the type I error, while achieving power approaches one, and validate the effectiveness of our test through numerical simulations. In real data analysis, we apply DRGCT to revisit the price-volume relationship problem in the stock markets of America, China, and Japan.

Problem

• Proposes doubly robust Granger causality test using deep learning
• Handles large lag orders while reducing dimensionality curse
• Provides efficient bootstrap method for critical value computation

Innovation

• Deep learning based doubly robust test
• Parametric convergence rate via neural networks
• Multiplier bootstrap for efficient critical values