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.

翻译：格兰杰因果关系在从自然科学到社会科学的诸多应用中（包括基因组学、神经科学、经济学和金融学）被广泛用于分析时间序列数据。因此，格兰杰因果关系检验数十年来一直是计量经济学家关注的主要问题之一。借助近年来深度学习领域的理论突破，我们提出了一种双重稳健的格兰杰因果关系检验方法。我们的方法具有若干关键优势。首先，最直接的好处是面向用户：DRGCT允许用户处理较大的滞后阶数，同时缓解传统非线性格兰杰因果关系检验通常面临的维度灾难问题。其次，基于神经网络为时间序列引入一种达到参数收敛率的双重稳健检验统计量，不仅为计量经济学中的非参数推断提出了新范式，也拓宽了深度学习的应用范围。第三，结合双重稳健方法的乘数自助法，为获取临界值提供了一种高效途径，有效减少了计算时间并避免了冗余计算。我们证明了该检验在渐近意义上控制了第一类错误，同时其功效趋近于1，并通过数值模拟验证了检验的有效性。在实际数据分析中，我们应用DRGCT重新研究了美国、中国和日本股票市场的价量关系问题。