Topology data analysis of critical transitions in financial networks

TL;DR

This paper introduces a topology data analysis method that uses persistent homology to detect early signs of critical transitions in financial networks by analyzing time-dependent correlation structures.

Contribution

It presents a novel approach combining topological data analysis with financial network analysis to identify early warning signals of financial crises.

Findings

Detected early signs of the 2007-2008 US financial crisis

Demonstrated the effectiveness of persistent homology in financial data

Provided a new tool for monitoring financial stability

Abstract

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.