MORA: Correcting Time Series Forecasts with Coarse Future Signals

Recent architectural advances have improved time-series forecasting. However, our analysis of forecasters with diverse architectures reveals a common pattern: a substantial share of residual energy is concentrated in a small number of low-frequency components. Simple linear probes further show that the forecasters' historical inputs still contain predictive information about errors in the forecast mean. Building on these findings, we propose Model-Output Residual Adaptation (MORA), a model-agnostic residual adapter that refines the outputs of frozen forecasters without requiring additional inputs. MORA estimates segment-wise means of the target sequence through structural extrapolation and learned estimation, rather than directly predicting backbone-specific residuals. It then converts discrepancies between these estimates and the corresponding statistics of the backbone forecast into stagewise corrections, scaling each update according to estimation reliability. Extensive experiments on twelve benchmarks with six forecasting backbones show average MSE reductions of $7.2\%$ for long-term forecasting and $28.1\%$ for short-term forecasting, with lower MSE in $96.2\%$ of the 288 evaluated cases. The benefits also extend to three time-series foundation models evaluated at different context lengths. Together, these results demonstrate that predictable coarse-scale residuals can be effectively exploited to improve existing forecasts. Code repository: https://anonymous.4open.science/r/MORA-B0B0/.