Which Histories Matter for Time Series Forecasting? Learning Predictive Relevance with Future Supervision

Abstract

Retrieval-augmented time-series forecasting typically selects historical examples by similarity between observed pasts, although similar pasts can evolve differently. We propose Predictive Relevance Retrieval (PRR), which uses realized future compatibility as privileged supervision to learn a retrieval function that remains strictly past-only at inference. PRR combines Pearson retrieval with a futuresupervised predictive representation to expand candidate support, then reranks the union using statistical and learned pair relations. Across six datasets and four long horizons, PRR improves Pearson retrieval in 23 of 24 conditions, reducing AnalogFutureMSE by 26.7% on average. A candidate-budget-matched variant, PRR-B100, retains nearly the same retrieval improvement while using at most 100 candidates at inference, showing that the gain is not explained simply by a larger candidate pool. We then connect the retriever to five frozen forecasting backbones using validation-calibrated trust. Downstream effects are heterogeneous, and calibration primarily reduces harmful retrieval use rather than making improved retrieval universally beneficial. These results show that predictive relevance and forecast utility are empirically distinct objectives.