{"title":"Topological variability in financial markets","authors":"Aaron D. Valdivia","doi":"10.3934/qfe.2023019","DOIUrl":null,"url":null,"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.","PeriodicalId":45226,"journal":{"name":"Quantitative Finance and Economics","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantitative Finance and Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/qfe.2023019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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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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