CoRA: Boosting Time Series Foundation Models for Multivariate Forecasting through Correlation-aware Adapter

Time-series foundation models (TSFMs) have achieved strong univariate forecasting through large-scale pre-training, yet effectively extending this success to multivariate forecasting remains challenging. To address this, we propose DualWeaver, a novel framework that adapts univariate TSFMs (Uni-TSFMs) for multivariate forecasting by using a pair of learnable, structurally symmetric surrogate series. Generated by a shared auxiliary feature-fusion module that captures cross-variable dependencies, these surrogates are mapped to TSFM-compatible series via the forecasting objective. The symmetric structure enables parameter-free reconstruction of final predictions directly from the surrogates, without additional parametric decoding. A theoretically grounded regularization term is further introduced to enhance robustness against adaptation collapse. Extensive experiments on diverse real-world datasets show that DualWeaver outperforms state-of-the-art multivariate forecasters in both accuracy and stability. We release the code at https://github.com/li-jinpeng/DualWeaver.

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: https://github.com/yyddou/CoReTTA

Direct forecasting has become a standard paradigm for multivariate time-series forecasting because it predicts the full future horizon in a single pass. However, its training objective is often still decomposed into pointwise errors such as MSE. Such objectives provide stable supervision, but they do not explicitly preserve the structure of the future trajectory: temporal coherence within each variable and relational consistency across variables can both be weakened. We propose CoRe, a model-agnostic learning objective for direct multivariate forecasting. CoRe replaces pointwise supervision with two output-space constraints: a frequency coherence loss that aligns predicted and target spectra, and a low-rank relational graph loss that matches sampled pairwise differences in a target-derived PCA subspace. The resulting objective introduces no trainable parameters and can be applied to existing forecasting backbones by changing only the loss. Experiments on standard benchmarks show that CoRe improves strong baselines, compares favorably with recent forecasting objectives, and remains effective across different backbones, datasets, and hyperparameter settings overall consistently.