RouteTS: Budgeted Spectral Component Routing across Time and Frequency Domains for Time Series Forecasting

Time-domain and frequency-domain predictors offer complementary inductive biases for recurring patterns and localized variations. However, existing architectures generally determine how the two domains are used through fixed design choices, rather than adapting spectral-component allocation to the input spectrum. We propose RouteTS, a lightweight framework that makes this allocation explicit through amplitude-based component routing. For each input window and variable, RouteTS ranks spectral components by amplitude, sends the Top-$K$ components to a shared complex-valued linear predictor, and transforms the complementary spectrum back to the time domain for modeling by a shared MLP. The dataset-specific routing budget $K$ is selected using only validation data, and varying $K$ yields time-only, mixed-domain, and frequency-only configurations within the same architecture. Across diverse benchmarks, RouteTS achieves the best average MSE on the majority of datasets while remaining among the most parameter- and memory-efficient models evaluated. Controlled analyses further show that the preferred allocation varies across datasets. In the mixed-domain cases examined, assigning dominant spectral components to the frequency predictor and the remainder to the temporal predictor improves accuracy over alternative component selections and reversed assignments.