Spectral Energy Allocation Enables Source-Free Domain Adaptation in Time Series Forecasting

Source-free domain adaptation (SFDA) adapts a pre-trained source model to an unlabeled target domain without access to source data. However, existing SFDA studies have predominantly focused on classification tasks, leaving time series forecasting (TSF), a fundamentally different problem with continuous outputs and complex temporal dependencies, largely unexplored. In this work, we identify unique characteristics and key challenges of SFDA in TSF: 1) forecasting labels correspond to future temporal segments of the same underlying signal, enabling us to split target input and construct a self-supervised learning task, thereby training an accurate short-term forecasting model to provide high-quality pseudo-labels; 2) however, such supervision remains inherently *local* rather than *global* for long-horizon source model adaptation. To fill this gap, we propose the notion of Spectral Energy Allocation (SEA) pattern, defined over a short-long signal pair. The SEA pattern provides a structured correspondence that bridges signals across different temporal horizons, enabling reliable short-horizon pseudo-labels to guide long-horizon adaptation. Extensive experiments demonstrate that our method substantially outperforms baselines across different forecasting backbones.