Geometric Observables for Financial Regime Detection

TL;DR

This paper introduces four geometric observables derived from spectral embeddings of equity returns to detect financial regime shifts, demonstrating superior performance over classical and machine learning baselines across multiple crises.

Contribution

It proposes a novel geometric approach for regime detection using spectral embedding observables, with an unsupervised score construction and hyperparameter tuning.

Findings

Berry Phase Rate achieves median Cohen's d = 0.72 in out-of-sample tests.

Reduced State Purity shows highest in-sample separability with d = 0.83.

Geometric and classical channels are largely uncorrelated, capturing distinct risk signals.

Abstract

We extract four geometric observables -- Berry Phase Rate, Spectral Entropy, Reduced State Purity, and Hamiltonian Sensitivity -- from a learned spectral embedding of equity-index returns and evaluate them as regime-shift detectors against 46 classical and machine-learning baselines on 17 historical crises spanning 2000-2024. Under walk-forward nested hyperparameter selection on nine labelled windows, the Berry Phase Rate achieves an unbiased out-of-sample median Cohen's $d = 0.72$ (95% percentile-bootstrap CI $[0.34, 1.18]$, 10,000 resamples) and produces approximately 67% fewer false alarms per year than a label-supervised Random Forest (1.2 vs. 3.6 per year). Reduced State Purity attains the highest in-sample separability of any method ($d = 0.83$), tied closely by the Absorption Ratio ($d = 0.80$); geometric and classical channels are largely uncorrelated (mean $|\rho| \approx 0.22$), suggesting they capture distinct risk signals. Score construction is unsupervised; hyperparameter selection is the only supervised step.