Topological variability in financial markets

Abstract

We investigate market crashes and downturns through the lens of persistent homology and persistence landscape norms. Using individual stock price data from Yahoo! Finance, we find that the variation in the persistence landscape norm as well as other measures of persistence exhibit a marked increase followed by a decline prior to historic incidents. We show that basic descriptions of persistent homology may be useful in addition to more sophisticated tools like the persistence landscape norm.

Keywords

• early warning signals
• topological data analysis
• dynamical systems
• data analysis
• quantitative finance