DSR-TSF: Spectrum-Driven Dynamic Routing for Efficient Long-Horizon Time Series Forecasting

Long-horizon time series forecasting requires a careful balance between predictive accuracy and computational cost. Segmented temporal modeling has therefore become a practical strategy for reducing the burden of long-range prediction. However, real-world time series often contain superposed multi-periodic components, whose spectral structures vary across time, variables, and samples. Such variability limits fixed aggregation or frequency-modeling mechanisms, making them less adaptive to non-stationary periodic patterns and potentially causing informative components to be attenuated over long forecasting horizons. To address this limitation, we propose DSR-TSF, a spectrum-driven dynamic routing framework for long-horizon forecasting. DSR-TSF adaptively selects and combines multiple period-specific branches conditioned on the spectral characteristics of the input sequence, thereby improving the model's ability to capture non-stationary periodic structures. It further learns period-aware dynamic weights to modulate the contributions of multi-periodic patterns while retaining the segmented prediction structure. Without complex resampling or explicit period alignment, DSR-TSF provides a compact mechanism for modeling spectral heterogeneity and achieves competitive performance across seven datasets with diverse dimensionalities and temporal characteristics.