Two-scale topological momentum and persistence of stress regimes in correlation networks: evidence from equity markets

We apply persistent homology to the time-varying correlation network of 49 Fama –French industry portfolios (1976–2026) to study synchronization transitions associated with market stress. Vietoris–Rips filtrations on rolling Mantegna distance matrices capture one-dimensional homological cycles (H1) that are associated with intransitive triples of sectors—configurations where two pairwise correlations are strong while the third remains relatively weak. The analysis reveals a two-scale topological structure:stress episodes amplify intransitivity among the most strongly correlated industries while dissolving it among weakly and moderately correlated ones. Because static topological indicators are highly collinear with average correlation, we shift attention to the momentum of topological reorganization. Using strict temporal separation and moving-block bootstrap validation, we find that the standardized rate of change in the persistence-weighted mean cycle birth parameter provides information beyond standard synchronization metrics, improving forecasts of stress onset. Decomposing cycles into sectoral triples maps abstract topology onto interpretable sectoral linkages. The method avoids look-ahead bias and applies to other domains with time-varying correlation networks.