Complementary Retrieval Geometries for Enhancing Multivariate Time Series Forecasting

Retrieval-augmented forecasting provides multivariate time-series forecasters with additional evidence by reusing trajectories that follow similar historical states; its effectiveness depends on how predictive historical similarity is defined. Existing methods typically organize retrieval around one principal criterion, causing a target variable's temporal shape and its dynamic role in a multivariate system to share the same similarity definition. We propose CoReG, a complementary retrieval framework for multivariate time-series forecasting. CoReG constructs two semantically distinct retrieval geometries: TimeGeo matches the target variable's multiscale temporal shape, while RoleGeo matches its system role using stable cross-variate relations and time-aligned role responses. The two paths independently retrieve the target variable's own historical future segments, form separate views relative to the same frozen backbone forecast, and produce the final prediction through symmetric merging. Across ten datasets and six forecasting backbones, CoReG improves both MSE and MAE in 58 of 60 paired settings, with mean relative reductions of 14.94% and 10.52%, respectively. Anonymous code is available at https://anonymous.4open.science/r/CoReg-3CCD/.