Topology data analysis of critical transitions in financial networks

2017/01/21 by Gidea, Marian
#Dynamical Systems (math.DS) #FOS: Economics and business #FOS: Mathematics #FOS: Physical sciences #Mathematical Finance (q-fin.MF) #Physics and Society (physics.soc-ph)

paper · doi:10.48550/arxiv.1701.06081

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.

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