Recursive deep learning with multi-scale attention for energy demand dynamics

• Fully learnable filters adapt to nonstationary and multi-scale signal dynamics. • Joint training of denoising and modeling enhances end-to-end accuracy and stability. • Entropy-aware gating fuses multi-stage forecasts with uncertainty-based weighting. • Delivers robust energy price forecasting under volatility and regime shifts. • Achieves up to 85% RMSE and 99% MAPE reduction over 50 existing models. Nonstationary and multi-scale time series challenge traditional decomposition-based and denoising techniques. These approaches often rely on fixed transformations or shallow residual modeling, limiting adaptability to evolving dynamics likes energy price forecasting. This work introduces an end-to-end recursive deep learning architecture that preserves the classical estimation loop while rendering all state-space parameters data-adaptive at every stage and time step. The parameters are synthesized by a lightweight neural generator conditioned on recent residual behavior and cross-scale context, enabling reconfiguration as regimes shift. Robustness is ensured through two design choices: a stability-preserving parameterization of state evolution that prevents drift and explosions, and innovation-driven, heteroskedastic noise modeling that automatically adjusts to volatility. At each stage, a trend is extracted, modeled by a shared deep multilayer perceptron (DMLP), and fused through an entropy-aware module that weights stage contributions, yielding a closed loop that progressively removes structure from the residuals. On the WTI crude oil dataset, compared to a baseline DMLP (MAE = 1.879, MAPE = 1.825 %, RMSE = 2.457), the proposed model achieved a 57.1 % reduction in MAE, 56.7 % in MAPE, and 58.0 % in RMSE (MAE = 0.806, MAPE = 0.787 %, RMSE = 1.031). It also outperformed over 50 state-of-the-art models, achieving up to 85 % lower RMSE and over 99 % reduction in MAPE. The framework is compact, reproducible, and suitable for energy-economics analytics under regime shifts and noise.