Real-world time series inherently intertwine global periodic structures with localized non-stationary variations. Existing approaches process these heterogeneous dynamics within a single computational domain, incurring fundamental limitations: time-domain models suffer from periodic misalignment over long horizons, while frequency-domain models over-smooth transient spikes. We argue that the optimal computational domain is not a property of the model, but of the data itself. Based on this principle, we propose RouteTS, a unified forecasting framework that partitions the frequency spectrum via amplitude routing and delegates components to their mathematically optimal domains. Dominant frequencies are processed by a complex-valued linear predictor in the frequency domain to preserve periodic structure, while residual spectral energy is reverted to the time domain and modeled by a lightweight MLP for local variations. Extensive experiments demonstrate that RouteTS achieves competitive prediction accuracy across diverse real-world datasets, with routing decisions guided by the underlying spectral signature. Furthermore, the lightweight design of RouteTS provides significant computational efficiency advantages, offering a principled solution to the longstanding dilemma between global periodicity and local transience.

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