From Black-Box AI to GARCH: Forecasting Gains and the Limits of Structural Translation

Abstract

Machine-learning models often improve volatility forecasts, but it is unclear whether their predictive information can be translated into stable economic mechanisms. This paper treats that distinction as an empirical identification problem. A nonlinear AI teacher forecasts daily range-based variance for four equity indices, while constrained state-dependent GJR-GARCH students attempt to absorb the teacher's information through interpretable ARCH, persistence, and leverage channels. The design separates predictive qualification, information transfer, and structural identification. Boosting teachers deliver double-digit out-of-sample QLIKE gains in all eight market-proxy comparisons, all favored by HAC-robust Diebold–Mariano tests. The ranking survives temporal partitions, alternative losses, moving-block inference, a feed-forward neural teacher, and a fully trained GRU teacher. Yet teacher guidance adds at most 0.11% over an otherwise identical linear-gate student. A medium-complexity nonlinear gate produces essentially no retention under the primary Parkinson target and only small, market-specific retention under Garman–Klass. Separately, ordered Markov-switching GJR anchors fail the predeclared identification gate in every market. The evidence therefore establishes a student-class-specific structural translation gap: AI predicts volatility more accurately, but its gain is only weakly and inconsistently retained by the tested two-anchor GJR gates and is not uniquely represented by identified regime anchors. GARCH is not obsolete; it remains the transparent benchmark that reveals the boundary between prediction and explanation.

Author abstract from the research manuscript. Typography and line breaks have been normalized; the linked source may show a different manuscript version.