Spectral Dynamics or Structured Linear Maps? Tiny Source-Only Time-Series Transfer

Can a model trained on one time-series dataset forecast an unseen dataset without target fitting? We study this question under a strict source-trained, target-free protocol using DynaFK, a compact forecaster that combines a seasonal anchor with a phase-dependent residual. At any fixed horizon, its encoder, diagonal recurrence, and decoder compose exactly into a phase-specific linear map. This motivates a matched direct control: with 397 real scalars it matches DynaFK at $H=96$, while larger linear and spectral models can improve accuracy at higher storage cost. The recurrence’s clearest benefits are horizon-independent parameter storage and execution across different channel counts. Source choice and horizon still change the ranking, so the results describe an accuracy–storage–portability trade-off rather than a universal advantage for spectral dynamics.