Abstract Time-series forecasting plays a critical role in applications such as smart grids, financial markets, weather prediction, and industrial monitoring. However, most deep learning models struggle under non-stationary conditions involving concept drift, abrupt regime changes, and noise-induced disturbances. This paper proposes a Dual-Stage Deep Learning Forecasting Framework (DS-DLFF) combining: a Variational Mode Decomposition (VMD)-based preprocessing module for decomposing non-stationary time-series into intrinsic mode components, and a Transformer-LSTM hybrid architecture that captures long-range dependencies and local temporal patterns within each decomposed component. A drift-adaptive calibration layer is introduced to detect distribution shifts using Maximum Mean Discrepancy (MMD) and dynamically update model parameters. Experiments conducted on four real-world datasets—electricity load, financial stock indices, traffic speed, and environmental pollution—demonstrate that DS-DLFF achieves significant improvements in RMSE, MAE, and MAPE compared to state-of-the-art baselines (Tables 2-4). This framework provides a robust forecasting solution for non-stationary environments, outperforming both classical ML models and advanced DL architectures.
Revathi, et al. (Sat,) studied this question.