We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological structures. We compute the persistent homology associated to these structures in order to track the changes in topology when approaching a critical transition. As a case study, we investigate a portfolio of stocks during a period prior to the US financial crisis of 2007-2008, and show the presence of early signs of the critical transition.
@article{arxiv.1701.06081,
title = {Topology data analysis of critical transitions in financial networks},
author = {Marian Gidea},
journal= {arXiv preprint arXiv:1701.06081},
year = {2017}
}