Unveiling complex nonlinear dynamics in stock markets through topological data analysis

Abstract

Testing and characterizing nonlinear serial dependence in financial time series constitutes a critical research focus, extensively applied in examining weak-form market efficiency. This study demonstrates ATCC’s capability to capture nonlinear dependence and employs it to analyze equity market return series. Our findings reveal that rolling-window ATCC can characterize high-resolution dynamics of dependence. For instance, using minute-level data, we document how the Russia–Ukraine conflict information significantly impacted dependence structures in the Chinese market. Furthermore, based on daily index data, the 2025 Trump tariff policies are shown to have substantially influenced dependence patterns in both Chinese and U.S. market indices. Notably, through combined ATCC and linear modeling of SSE 50 constituent returns, we find that while linear models adequately characterize dependence in most daily returns, a minority of stocks exhibit nonlinear serial dependence. This research establishes an ATCC-based analytical framework, providing an effective quantitative tool for investigating nonlinear serial dependence and its high-resolution dynamics.