Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, machine learning, computer vision, computational biology, brain functional networks, financial haze detection, etc. this article, we will focus on stock markets demonstrate how TDA can be useful regard. We first explain signatures that detected using TDA, for three toy models changes. then showed to go beyond network concepts like nodes (0-simplex) links (1-simplex), standard minimal spanning tree or planar maximally filtered graph picture cross correlations markets, work with faces (2-simplex) any k -dim simplex TDA. By scanning through a full range correlation thresholds procedure called filtration, were able examine robust features (i.e. less susceptible random noise) higher dimensions. To advantages collected time-series from Straits Times Index Taiwan Capitalization Weighted Stock (TAIEX), computed barcodes, persistence diagrams, entropy, bottleneck distance, Betti numbers, Euler characteristic. found during periods market crashes, groups become as vary characteristic correlation. For both consistent associated crashes characteristics, agreement our theoretical expectations.