Correction-space Cross-variate Interaction for Test-time Adaptation in Time Series Forecasting

Test-time adaptation (TTA) is a promising paradigm for handling distribution shift in time-series forecasting (TSF), where models adapt at inference time, often leveraging delayed observed data to refine predictions. In the multivariate setting, distribution shifts often exhibit cross-variate dependencies, yet existing TSF-TTA methods adapt each variate independently and ignore this cross-variate structure. Exploiting such structure motivates cross-variate interaction, but coupling variates through backbone predictions introduces direct pathways for mixing uncorrected errors across variates, a concern under the delayed supervision of TSF-TTA. We identify the interaction space as a key design choice, and show that acting on adapter corrections that refine backbone outputs, the correction space, rather than on the predictions themselves, avoids directly propagating backbone errors across variates. We build on this to propose CoRe (Correction-space Interaction Refinement), realizing correction-space interaction through (i) Shared-anchor Correction Refinement (SCR), which combines each variate's correction with a shared anchor through a parameter-efficient bottleneck, and (ii) input-conditioned spectral gating, which adaptively modulates the refinement from the current input window. Across seven backbones, six datasets, and four prediction horizons, CoRe reduces MSE by 25.82% on average over backbones and 10.57% over the state-of-the-art TSF-TTA method, with stronger gains at medium-to-long horizons and modest computational overhead. Data and code are available at: anonymous.4open.science/r/CoRe-TTA-CD98.