Dimensional Collapse and Anomalous Scaling in Multi-Asset Financial Markets: Real-Time Early Warning via Topological Phase Space Manifolds
Year: 2026
Type: preprint
Abstract: We develop and empirically test a real-time early-warning framework for systemic liquidity stress in multi-asset equity markets based on a topological phase-space information measure. The framework jointly tracks anomalous temporal memory through the Hurst exponent and collective spatial compression through the effective manifold dimension derived from the sample covariance spectrum. Using daily market data from leading S&P 500 constituents across four sectors, we compare a normal market regime with the systemic liquidity crash of February–March 2020. During the crash, temporal persistence increases while the effective manifold dimension collapses, indicating that diversified market dynamics become dominated by a collective liquidation mode. We argue that the joint evolution of increasing temporal persistence and collapsing effective dimension provides a potentially actionable early-warning signature preceding market troughs. Conversely, elevated manifold dimension combined with moderate temporal persistence characterizes a healthier market state with more diversified sectoral degrees of freedom. We further outline robustness tests based on covariance shrinkage, rank correlations, random-matrix null models, and bootstrap confidence intervals, while discussing limitations related to non-stationarity, heavy tails, and the finite crash window.
Author: Pirolo, Andrés
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7210269378
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