A stacking model integrating GARCH and LSTM with feature interactions for time series volatility prediction

Abstract

Volatility forecasting remains a cornerstone of quantitative finance, underpinning risk management, portfolio optimization, and regulatory oversight. This study introduces a novel stacking model that integrates the generalized autoregressive conditional heteroskedasticity (GARCH) framework with long short-term memory (LSTM) networks to capture both econometric structure and nonlinear temporal dependencies in financial time series. Unlike conventional hybrid approaches that sequentially cascade outputs, the proposed framework employs GARCH and LSTM as parallel base learners, with their predictions intelligently fused through a meta-learner that exploits feature interactions and cross-model synergies. The empirical evaluation benchmarks the stacking ensemble against state-of-the-art alternatives, including DLINEAR, CKAN, N-BEATS, and individual GARCH and LSTM specifications across multiple performance metrics. Results demonstrate consistent superiority across RMSE, MAE, accuracy, RAMP, geometric mean, Hausdorff distance, and AUC metrics, validating the synergistic benefits of integrating econometric and machine learning paradigms within a theoretically grounded architecture. The model’s superior performance stems from leveraging GARCH’s parametric efficiency in modeling volatility clustering while harnessing LSTM’s capacity to capture complex nonlinear temporal patterns. Beyond methodological contributions, the framework offers practical value for enhancing systemic risk monitoring, improving stress testing frameworks, and optimizing investment strategies across diverse market conditions. The demonstrated robustness across different market regimes underscores its potential for adoption in both routine operations and crisis contexts. This research establishes stacking-based ensemble modeling as a powerful paradigm for advancing volatility prediction and provides a foundation for next-generation financial forecasting systems.

HIGHLIGHTS • Stacked GARCH-LSTM captures volatility clustering and long-term dependencies. • Interaction layer models relationships of GARCH indicators with LSTM features. • Combines econometric and deep learning, boosting predictive accuracy on real data. • Stacking framework explains GARCH while utilizing LSTM learning capabilities.