Autoregressive mutual-information networks for detecting and forecasting nonequilibrium regimes in oil–equity markets

Financial markets are prototypical nonequilibrium complex systems in which shocks propagate through time-varying, nonlinear channels that linear correlation misses. We develop a unified statistical-mechanical framework to study oil–equity interdependence over 2015–2025 by coupling (i) rolling mutual-information (MI) dependency networks estimated with the KSG k -NN estimator and filtered via PMFG to extract a sparse backbone, (ii) turbulence and nonlinear-dynamics diagnostics (Mahalanobis distance, permutation entropy, largest Lyapunov exponent) that quantify departures from typical states, and (iii) regime detection via a z -scored composite and PELT segmentation, with forecasting through an MI-informed network autoregression. We uncover a persistent, tightly knit equity core anchored by U.S. benchmarks and a structurally peripheral oil block that couples more strongly to energy equities than to broad markets; network density remains ∼0.62–0.65 while clustering stays high (∼0.75–0.80), with episodic rewiring during stress (COVID-19; 2022–2024). Turbulence spikes coincide with entropy dips and weaker Lyapunov exponents, signaling transient complexity loss. Embedding MI network spillovers improves point forecasts relative to a VAR with a lower RMSE/MAE. The framework is robust to MI estimation, filtering, and covariance regularization and yields compact early-warning indicators of fragility for portfolio and systemic-risk surveillance. We also quantify motif over/under-expression (triangles and wedges under a label-shuffle null), showing persistent equity-clique closure and episodic equity–oil mixing aligned with detected regimes.