Change Point Detection in Financial Market Using Topological Data Analysis
Jian Xi Yao, Jingyan Li, Jie Wu, Mengxi Yang, Xiaoxi Wang · Systems · 2025
Change points caused by extreme events in global economic markets have been widely studied in the literature. However, existing techniques to identify change points rely on subjective judgments and lack robust methodologies. The objective of this paper is to generalize a novel approach that leverages topological data analysis (TDA) to extract topological features from time series data using persistent homology. In this approach, we use Taken’s embedding and sliding window techniques to transform the initial time series data into a high-dimensional topological space. Then, in this topological space, persistent homology is used to extract topological features which can give important information related to change points. As a case study, we analyzed 26 stocks over the last 12 years by using this method and found that there were two financial market volatility indicators derived from our method, denoted as L1 and L2. They serve as effective indicators of long-term and short-term financial market fluctuations, respectively. Moreover, significant differences are observed across markets in different regions and sectors by using these indicators. By setting a significance threshold of 98 % for the two indicators, we found that the detected change points correspond exactly to four major financial extreme events in the past twelve years: the intensification of the European debt crisis in 2011, Brexit in 2016, the outbreak of the COVID-19 pandemic in 2020, and the energy crisis triggered by the Russia–Ukraine war in 2022. Furthermore, benchmark comparisons with established univariate and multivariate CPD methods confirm that the TDA-based indicators consistently achieve superior F1 scores across different tolerance windows, particularly in capturing widely recognized consensus events.