CoSTAR: Common-State Adaptive Refinement for Multivariate Time Series Forecasting

Multivariate time-series forecasting is central to applications such as energy management, traffic prediction, and weather analysis, where channels exhibit both shared and channel-specific dynamics. Existing forecasters capture these dependencies through their internal architectures; however, incorporating an additional refinement signal commonly requires altering the backbone. To address this limitation, we propose CoSTAR (Common-State Adaptive Refinement), an external module that operates only through a forecaster's input and output interfaces. CoSTAR factorizes the history into a common component and a residual input, summarizes the common trajectory with four window-level statistics, and decodes a gated residual forecast correction. We evaluate CoSTAR on eight long-term benchmarks and four PEMS traffic datasets. Across paired comparisons of five backbones on six datasets, CoSTAR reduces horizon-averaged MSE in 29 of 30 backbone–dataset pairs, with one tie at the reported precision; the largest reduction is 72.4% for SparseTSF on PEMS04. Ablations, five-seed analyses, and frozen-backbone experiments further characterize the contribution and scope of the design.