Academic Report of School of Mathematical Sciences [2026] No. 067

(Series Report for High-Level University Construction No. 1326)

Title：Deep learning based doubly robust test for Granger causality

Speaker：Xiaojun Song, Associate Professor (Peking University)

Time：15:00-16:00, July 8, 2026

Location：Room 514, Huixing Building, Yuehai Campus, Shenzhen University

Abstract:Granger causality is a fundamental concept for analyzing dynamic relationships in time series data, with widespread applications across the natural and social sciences, including genomics, neuroscience, economics, and finance. Consequently, nonparametric Granger causality testing has remained a central focus in econometrics for decades. Leveraging recent theoretical breakthroughs in deep learning, we propose a novel deep learning-based doubly robust Granger causality test (DRGCT). Our methodology offers several compelling advantages. First, for empirical practitioners, DRGCT naturally accommodates large lag orders, effectively circumventing the curse of dimensionality that inherently cripples traditional smoothing-based nonparametric tests. Second, from a theoretical perspective, our doubly robust moment construction elegantly neutralizes the slow convergence rates of deep neural networks. This allows the test statistic to achieve a parametric convergence rate, thereby establishing a new paradigm for valid nonparametric inference using deep learning in econometrics. Third, we develop a computationally efficient multiplier bootstrap procedure that flawlessly replicates the complex temporal covariance structure without redundant network retraining, further robustifying our test against general non-Markovian dynamics via a block-based extension. Theoretically, we prove that our test asymptotically controls the type I error, achieves an asymptotic power of one against fixed alternatives, and possesses non-trivial local power against alternatives converging at the optimal parametric rate $n^{-1/2}$. Finally, we validate the finite-sample performance of DRGCT through extensive numerical simulations and apply it to revisit the intricate price-volume relationships in the stock markets of the United States, China, and Japan.

Speaker Profile：Xiaojun Song is an associate professor and Ph.D. advisor in the Department of Business Statistics and Econometrics at the Guanghua School of Management, Peking University. He holds a Ph.D. in Economics from Carlos III University of Madrid, Spain. His primary research interests include theoretical econometrics—such as nonparametric and semiparametric methods, hypothesis testing, and bootstrapping—as well as the applications of econometrics. His papers have been published in international journals such as Annals of Applied Statistics, Biometrics, Econometric Reviews, Econometric Theory, Journal of Applied Econometrics, Journal of Business & Economic Statistics, Journal of Econometrics, Journal of Time Series Analysis, and Oxford Bulletin of Economics and Statistics. He has led and participated in General and Key Projects funded by the National Natural Science Foundation of China. He has received honors including Peking University’s Outstanding Class Advisor, Outstanding Ph.D. Thesis Advisor, and the Peking University Cai Yuanpei Aesthetic Education Teaching Award. Since January 2020, he has served as Associate Editor of Economic Modelling.

Faculty and students are welcome to attend!

Invited by: Zongliang Hu

School of Mathematical Sciences

June 25, 2026