Estimate What Repeats, Learn What Remains: Post-Hoc Correction of Frozen Time Series Forecasters

Deep forecasters and pretrained foundation models have made time-series fore- casting far more accurate, yet the errors of a trained model are not unstructured noise. Whether a forecaster overpredicts or underpredicts often depends on where the target falls within the daily cycle and on how many steps ahead the forecast is made, and the same dependence is already present on the training data. Exist- ing post-hoc correctors lower the average error but leave much of this recurring pattern in place. We introduce LIRA (Lookup and Input-conditioned Residual Ad- justment), a correction framework for frozen forecasters that first estimates what repeats and then learns what remains. A recurring error lookup pools historical residuals by target cycle position and forecast lead, and a channel-shared linear head is trained on the residual left after the lookup. Because the lookup stores statistics rather than learned weights, newly observed forecast errors update the lookup alone, so online correction needs neither additional backbone calls nor gradient optimization. Across five task-specific backbones and four foundation models, online LIRA lowers horizon-averaged MSE in every backbone–dataset pair, by 8.77% and 17.64% on average, and matches or outperforms the post-hoc correctors δ-Adapter and PIR in most task-specific pairs, with lower correction computation and storage costs.