Attributing Forecast Gains in Hybrid GARCH–Deep Learning Models: A Critical Review of Architecture, Information, and Evaluation

Abstract

Hybrid GARCH–deep learning models are often presented as a cumulative progression in which econometric structure and neural flexibility jointly improve volatility forecasts. This critical review asks a narrower question: what does the connection itself add? A structured search and citation-chaining exercise retained 30 qualifying studies published or circulated between January 2018 and 28 August 2026: 27 peer-reviewed articles and three working papers. Seventeen use state transfer, six use forecast or error combination, and seven use recursion embedding. The evidence supports conditional complementarity but not a monotone ranking of integration depth. Reported gains commonly bundle architecture with unequal information, search effort, targets, validation windows, and stress-period composition. The hybrid attribution framework therefore defines performance contrasts on a common expected-loss scale and translates them into information-matched comparisons, nested ablations, common tuning rules, and identical forecast origins. Four patterns emerge: GARCH-derived states are representations rather than new information; simple diversification is an underused benchmark; embedded recursions improve coherence but raise identification costs; and point-volatility gains need not improve tail calibration or economic value. The principal limitations are partial 2026 coverage, English-language discovery, single-author coding, heterogeneous outcomes, and reliance on reported rather than replicated results. The next advance depends less on another hybrid label than on identifying when, why, and for which endpoint the econometric–neural link adds value.

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