Academic Report of the School of Mathematical Sciences [2025] No. 093  

(High-Level University Construction Series Report No. 1115)  

Lecture Title: A data-driven approach for independence testing in multivariate time series based on Chatterjee's rank correlation  

Lecturer: Professor Wang Guochang (Jinan University)  

Lecture Time: October 14, 2025, 16:00-17:00 (afternoon)  

Venue: Conference Room 303, Alumni Plaza  

Abstract:  

Verifying whether a multivariate time series follows an independent and identically distributed (i.i.d.) sequence is a critical issue.This paper introduces a novel method for testing this assumption by analyzing the dependency structure inherent in the data. Specifically, we utilize Chatterjee's rank correlation to develop a new analytical tool, termed the auto-Chatterjee's rank correlation matrix (ACRCM). Each element of the ACRCM quantifies Chatterjee's rank correlation, effectively capturing nonlinear dependencies within the observed series. We develop an ACRCM-based statistic with fixed order for testing independence in multivariate time series, which asymptotically follows a chi-squared distribution under the assumption of independence. Furthermore, we introduction a data-driven approach for automatically determining the optimal order based on the data characteristics.This data-driven approach offers three key advantages:first, it eliminates the need for manually specifying the order, as the optimal order is automatically selected based on the data;second, under the null hypothesis, the selected order is one, and the chi-square distribution has degrees of freedom correspond to the square of the data dimension;third, the proposed data-driven approach demonstrates superior sensitivity to detecting high-order dependencies.We rigorously derive the asymptotic properties of the proposed method and validate its effectiveness through extensive simulation experiments.

Lecturer’s Biography:  

Wang Guochang is a Professor and Doctoral Supervisor at the Department of Statistics and Data Science, School of Economics, Jinan University. His main research directions include functional data, time series, and machine learning. To date, he has published more than 30 papers in important academic journals such as JoE, JBES, Sinica, and Scandinavian Journal of Statistics. He has presided over 4 national-level projects and 4 provincial-level projects. He serves as Vice Director of the China Tourism Big Data Association, and Standing Director and Secretary-General of the Guangdong Provincial Association of Applied Statistics.  

Faculty and students are welcome to attend!  

Inviter: Wang Jiangzhou  

School of Mathematical Sciences  

September 30, 2025