2026/04/07 by Bernd von Mallinckrodt · 1 voice
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Complex Systems and Dynamics #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19453102
openalex publication_date 2026/04/07 · openalex created_date 2026/04/08 · openalex updated_date 2026/07/01
This preprint presents an empirical evaluation of structural compression Φ(t) as an early warning signal (EWS) for financial market transitions. Structural compression is defined as the effective rank of a rolling, regularized covariance matrix and captures changes in the geometric organization of multivariate systems beyond classical univariate indicators. The analysis is conducted on daily log-returns of S&P 500 sector ETFs and covers two independent crisis events with distinct onset dynamics: the 2008 Global Financial Crisis and the 2020 COVID-19 market crash. Indicators are computed using rolling windows (L = 80, 120, 160 trading days) with covariance estimation via the Ledoit–Wolf shrinkage method. Trend significance is assessed using Kendall’s τ and validated against Iterative Amplitude Adjusted Fourier Transform (IAAFT) surrogates to account for autocorrelation and distributional structure. Results show that Φ(t) exhibits surrogate-significant monotonic trends in both crisis events, while classical indicators (variance, PC1 variance, AR(1)) do not achieve consistent significance across events. The composite indicator T(t) = R(t)/Φ(t) further amplifies the signal. The findings suggest that structural changes in covariance geometry may provide information about approaching systemic transitions not fully captured by classical early warning signals. The analysis is retrospective and limited to two events; no claims of generality or predictive applicability are made. Further validation across additional systems and datasets is required. All code and data processing steps are fully reproducible and included in the accompanying materials. Primary keywords: early warning signals critical transitions structural compression effective rank spectral entropy Domain keywords: financial markets systemic risk S&P 500 covariance analysis Method keywords: multivariate time series Ledoit-Wolf IAAFT surrogate testing Kendall tau