Topological Early Warning of Equity Market Stress: Signal Selection and Transfer Across Industry Portfolios

This study examines whether changes in sectoral market structure can serve as early warningsignals for severe market crashes using topological data analysis (TDA). Features of persistenthomology and their temporal changes are derived from daily returns of the twelve Fama Frenchindustry portfolios in rolling time windows. The analysis covers the period 1932 to 2025 with 28event clusters, examining a search space of 9,408 candidates under false alarm constraints inseparate training, validation, and test splits. Null tests with randomly shifted event calendarsexamine the candidate selection and subsequent test performance separately. During the testperiod of 2010 to 2025, three of the four false alarm regimes considered achieve significant testperformance compared to the null model used. The warning system detects six out of nineevent clusters with a median lead time of 31 trading days. In the process, 48 false alarm daysoccur within 3,878 trading days. With this warning system, candidate selection remains stableeven when individual validation event clusters are omitted. In contrast, performance on thevalidation split was not statistically significant under the global null test, and no significantadditional benefit from ensembles was found. The transfer of its defined signal and alarm ruleswith local calibration yields significant results for 30, but not for 49, industry portfolios. Theresults support the early warning potential of selected topological signals in the U.S. marketunder investigation. However, the small number of events, the lack of statistical significance onthe validation split, and the inconsistent transfer to industry portfolios limit the generalizabilityof the findings.