One More Token: Patch-Boundary Revisions in Time-Series Foundation Models

Fixed-patch time-series foundation models group past observations into tokens before making a forecast. Adding one observation can create a new token and produce a sharp change in the prediction. We study this transition in Chronos-Bolt, TimesFM, and Moirai by extending the same history one observation at a time. Among the sampled local transitions, the token boundary has the largest average revision in 46 of 48 model, dataset, and horizon settings. Changing Moirai’s patch size moves the revision peak to the new boundary. An attention intervention shows that allowing other tokens to read the new token contributes to the change, with additional TimesFM experiments confirming the effect on previously unused series. We then explain how these revisions affect accuracy. An exact squared-error decomposition separates the size of the revision from its direction relative to the model’s existing error. On generated autoregressive series, Moirai’s revision corrects that error, with an expected-loss change 2.47% of the irreducible forecasting variance lower than at nearby non-boundary transitions. Real-data results show that the loss effect varies across models and datasets. Together, these findings connect a discrete change in input representation to both forecast revisions and their accuracy.