Future-distilled Spectral Enhancement for Long-term Time Series Forecasting

Long-term forecasters often over-smooth predictions, attenuating the mid- and high-frequency components that carry local dynamics. We propose FSE (Future-distilled Spectral Enhancement), a lightweight, model-agnostic post-hoc module that corrects this spectral bias without modifying or retraining the underlying forecaster. A future teacher branch encodes the ground-truth future spectrum during training, while a past student branch learns to infer a corresponding representation from the historical window alone; a non-contrastive dual-alignment objective transfers this privileged information without explicit negative sampling. At inference, only the student branch remains, guiding a bounded correction network that refines the frozen baseline's spectrum. Across seven benchmarks and six forecasting backbones, FSE improves accuracy in most settings and specifically reduces high-frequency error, with negligible inference overhead. Because it treats the backbone as a fixed black box, FSE is naturally positioned as a candidate adapter for frozen, pretrained time series foundation models, which we discuss as future work.