Information-Theoretic ESG Index Direction Forecasting: A Complexity-Aware Framework.

Sustainable finance exhibits non-linear dynamics, regime shifts, and distributional drift that challenge conventional forecasting, particularly in volatile emerging markets. Conventional models, which often overlook this structural complexity, can struggle to produce stable or reliable probabilistic forecasts. To address this challenge, this study introduces a complexity-aware forecasting framework that operationalizes information-theoretic meta features, Shannon entropy (SE), permutation entropy (PE) and Kullback-Leibler (KL) divergence to make Environmental, Social, and Governance (ESG) index forecasting more stable, probabilistically accurate, and operationally reliable. Applied in an emerging-market setting using Türkiye's ESG index as a natural stress test, the framework was benchmarked against a macro-technical baseline with a calibrated XGBoost classifier under a strictly chronological, leakage-controlled nested cross-validation protocol and evaluated on a strictly held-out test set. In development, the framework achieved statistically significant improvements in both stability and calibration, reducing fold-level dispersion (by 40.4-66.6%) across all metrics and enhancing probability-level alignment with Brier score reduced by 0.0140 and the ECE by 0.0287. Furthermore, a meta-analytic McNemar's test confirmed a significant reduction in misclassifications across the development folds. On the strictly held-out test set, the framework's superiority was confirmed by a statistically significant reduction in classification errors (exact McNemar