What question did this study set out to answer?

The aim is to create a robust forecasting framework that effectively handles non-stationary time-series data.

May 29, 2026Open Access

A Dual-Stage Deep Learning Framework for Robust Time-Series Forecasting Under Non-Stationary Conditions

Key Points

The aim is to create a robust forecasting framework that effectively handles non-stationary time-series data.
Developed a Dual-Stage Deep Learning Forecasting Framework (DS-DLFF) combining VMD for preprocessing and a transformer-lstm hybrid architecture.
Introduced a drift-adaptive calibration layer to detect and manage distribution shifts using Maximum Mean Discrepancy (MMD).
Applied framework to four real-world datasets including electricity load and stock indices.
DS-DLFF achieved significant improvements in RMSE, MAE, and MAPE compared to state-of-the-art baselines for the datasets evaluated.
Demonstrated better performance than both traditional machine learning models and advanced deep learning architectures in handling non-stationary data.

Abstract

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.

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