Topological variability in financial markets

Aaron D Valdivia; Aaron D Valdivia

doi:10.3934/QFE.2023019

Quantitative Finance and Economics

2023, Volume 7, Issue 3: 391-402. doi: 10.3934/QFE.2023019

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Research article

Topological variability in financial markets

Aaron D Valdivia ^,

Department of Mathematics, Florida Southern College, 111 Lake Hollingsworth Drive, Lakeland FL 33603, USA

Received: 06 June 2023 Revised: 25 July 2023 Accepted: 07 August 2023 Published: 11 August 2023
JEL Codes: C02, G15

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.
- early warning signals,
- topological data analysis,
- dynamical systems,
- data analysis,
- quantitative finance
Citation: Aaron D Valdivia. Topological variability in financial markets[J]. Quantitative Finance and Economics, 2023, 7(3): 391-402. doi: 10.3934/QFE.2023019

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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.

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