Learning Where Frozen Forecasters Fail: Residual-Based Retrieval Augmentation for Time-Series Forecasting

Retrieval-augmented generation (RAG) supports time-series forecasting by re- trieving historical trajectories and representations to inform predictions. However, the potential of historical evidence to refine a forecaster’s existing predictions by targeting its remaining errors remains underexplored. Such refinement builds on the temporal patterns already captured by the forecaster, while its histori- cal residuals provide model-specific evidence about the direction and magnitude of past errors. Using RAG to augment forecasting via residuals presents two challenges: identifying relevant historical errors when the current residual is un- observed, and determining their correction strength when historical and current prediction conditions differ. To address these challenges, we propose Residual- based Retrieval-Augmented Forecasting of Time-series (ResRAF), which organizes a frozen forecaster’s historical errors into a residual-based knowledge base. Its Residual-Aware Retriever learns from historical residual supervision to predict residual pattern representations from the current input and base forecast, then combines residual proximity with forecast-shape similarity to retrieve complete historical residual sequences. State-Adaptive Retrieval Calibration adjusts the con- tributions of these sequences according to the prediction states of both the current and historical instances, derived from observable input and forecast characteristics. The calibrated residuals are aggregated and added to the base forecast, with the forecaster remaining frozen and all additional components fitted on training data and fixed during evaluation. Experiments across multiple datasets, forecasting architectures, and prediction horizons show that ResRAF outperforms existing methods in forecasting accuracy.