Title:When Does Retrieval Help Time-Series Forecasting?

Abstract:Retrieval plug-ins supply a deep forecaster with information its lookback window cannot carry. Published evaluations report consistent gains, and each credits its own mechanism. We show that the benefit belongs instead to the operating point: the relation between window length $S$ and dominant seasonal period $L$, an axis the standard protocol never varies. Stratifying the evaluation by that relation exposes the regime. At $S{=}12$, a simple control that repeats the last observed period beats the six standard backbones, in aggregate, on four of seven benchmarks by $8\%$ to $44\%$ of MSE. It beats the strongest plug-in we run on ETTm1 and matches it on ECL. It is worse by up to $25\%$ on the three datasets whose training-split spectra lack a concentrated, shared period. A controlled synthetic sweep of horizon, period, and window shows the benefit boundary tracks the period (correlation $+0.71$), not the horizon ($-0.23$). A paired control with no phase to recover nearly erases the effect, consistent with phase starvation. Zero-shot pretraining does not escape it: a foundation model trails trained backbones by $22\%$ to $50\%$ on the periodic benchmarks. Within our instrument, exact lookup matches graph diffusion: the payoff is consulting the record, not the machinery on top. Two interpretable statistics, a trend test and a staleness rate, predict the sign of the per-cell benefit at $0.76$ accuracy under leave-one-dataset-out evaluation, a suggestive margin over the $0.69$ majority rule, where a 22-feature stack manages $0.57$. We propose no new plug-in. The contribution is the regime map, the protocol that reveals it, and two statistics that screen it before deployment. Code: this https URL.

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