TITLE:
Dynamic Causal Relationships in Stock Market: A Three-Dimensional Granger Causality Network Approach
AUTHORS:
Panmeng Huang, Yuan Liu, Huanghao Chen, Jerome Yen, Naixue Xiong, Hui Bu
KEYWORDS:
Granger Causality, Hang Seng Index, Gaussian Mixture Model, Multi-Layer Directed Causal Network
JOURNAL NAME:
Open Journal of Social Sciences,
Vol.14 No.4,
April
30,
2026
ABSTRACT: Traditional Granger-causality framework relies only on the movement of asset prices. However, clustering of stocks needs more information to identify the strength of their bonding, including but not limited to trading volume and volatility. In order to build a more robust portfolio formation framework, in this paper, a three-dimensional Granger-causality framework is proposed to study the dynamic causal relationships among stocks in the Hong Kong (SAR, China) stock market (HKG). Toda-Yamamoto Granger test (TY-Granger test) was conducted by using the constituent stocks of the Hang Seng Index (HSI). The data set contains the prices, trading volume, and volatility from February 2020 to December 2024, where 60 monthly Granger (involving approximately 20 trading days per month) causality networks were constructed. By combining each daily Granger causality matrix within that month using an e-value-based method, stocks were classified via multi-layer directed causal network feature extraction by Gaussian Mixture Model (GMM) based unsupervised clustering into three different types of clusters: Influential, Affected, and Isolated. Such classification has proven to be useful in supporting the formation of portfolio under different market conditions.