Ngoc Kim Khanh NguyenMarc Bui2022-10-172022-10-172021https://repository.vlu.edu.vn/handle/123456789/29210.6977/IJoSI.202112_6(6).0005"We investigate the collective behavior of a stock market by studying the dynamics of its representative index’s return, using the persistence diagram of the index return’s time-delay embedding, an approach of the Topological Data Analysis (TDA) in time series analysis. While the time-delay embedding captures the state space of the index return’s dynamics, the persistence diagram encodes the space's topological information under different spatial resolu-tions. Therefore, based on the changes in the point distribution of the persistence diagram over time, we propose a framework to detect its extraordinary movements. Our method provides a measure for the stability level of the mar-ket’s collective behavior. After applying this method for the daily return of the S&P 500 index from 1970 to 2020, we demonstrate that the measure efficiently tracks the changes in topological information of the index re-turn. Furthermore, we can capture major American recessions when the measure exceeds a threshold. A continuous and rapid increase of the measure approaching the threshold is considered a warning of a crisis. Hence, our method provides a technical indicator for systematic risk management."en-USanomalies detectionmarket indexpersistence diagramtime-delay embeddingResource Types::text::journal::journal article