Better on Average, Worse Locally: Interval Guarantees for Online Forecast Adaptation

An adaptive forecaster can improve total error while worsening a recent interval. We study a causal guard that bounds the eventual excess MAE of every interval of issued multi-horizon forecasts relative to a frozen reference, including intervals whose targets are not yet observed. For absolute loss, accounting jointly for the predictions that share a target makes each interval's feasible set a translated ${\ell }_1$ ball—exactly the forecasts that keep the guarantee for every completion of the pending targets—and under regular horizon-$H$ feedback the history compresses into two statistics and at most $H$ active constraints. A constructed example separates this exact accounting from any independent certificate by a factor of order $\sqrt{H}$. Replays on temperature, Exchange Rate, multivariate transit, Weather and electricity, including modern online adapters, show that unguarded adaptation often lowers mean error while a single interval absorbs a regression that grows $9$–$43$-fold with aggressiveness. The certificate removes it at a mean-MAE cost that is negligible or negative on temperature and material, but tunable through the allowance, on transit, Weather and electricity. Cheap independent guards match the exact guard in error: on the audited streams exact accounting accepts $1.4$–$1.7\times$ more of each candidate's correction without changing realized error, so the separation, genuine in the worst case, is operationally inert. We contribute an exact characterization of what every-interval protection allows and a measured account of what it costs.