Laplacian Spectra of Persistent Structures in Taiwan, Singapore, and US Stock Markets.

ABSTRACT: An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic. In all four crashes, a persistent gap opens up in the Laplacian spectra when we go from a normal phase to a crash phase. In the crash phase, the persistent structure associated with the gap remains distinguishable up to

SUBMITTER: Yen PT 

PROVIDER: S-EPMC10297551 | biostudies-literature | 2023 May

REPOSITORIES: biostudies-literature