Bridging the Experience Gap: Semantic Retrieval and Conditional Residual Transfer for Time Series Forecasting

Time series forecasting draws on historical observations, but abundant historical data does not necessarily provide relevant experience for a particular forecast. An entity may face conditions absent from its own history, while useful experience exists across other entities and contexts. Drawing on this experience presents two challenges: 1) identifying relevant historical cases through semantic connections rather than numerical similarity; 2) adapting their responses across differences in timing, magnitude, and shape to improve the target forecast. To address these challenges, we propose $\text{SCoRe}$, a plug-and-play framework for augmenting frozen forecasting models. It retrieves semantically analogous historical cases and adapts their forecast residuals to correct the target forecast. $\text{For semantic retrieval}$, a large language model jointly characterizes entity attributes, historical states, and known future conditions, exposing contextual connections that guide the retrieval of potentially transferable residuals. $\text{For response adaptation}$, the retrieved residuals are aligned with the target conditions. Learned directional gain estimates and candidate interactions then guide the joint selection and weighting of residual corrections. By combining semantic retrieval with explicit response adaptation and joint utility assessment, the framework enables forecast correction when direct historical matches are unavailable. Our evaluation examines forecasting accuracy, transfer across entities and contexts, and negative transfer across multiple forecasting backbones. Code is available at https://anonymous.4open.science/r/TextRAG-F67B.