Variable Subset Forecasting (VSF) poses critical challenges in time series analysis when entire variables become unavailable during inference. Existing imputation methods relying on inter-variable correlations fail catastrophically in VSF due to two inherent limitations: (1) Missing variable collapse, where the complete absence of certain variables invalidates correlation-based dependency learning, and (2) Temporal covariate shift, where time-evolving data distributions destabilize correlation patterns learned from training data. To address these fundamental issues, we propose Generative Imputation with Multi-level Causal Consistency (GIMCC ), establishing causality-driven imputation as the first principled solution for VSF. Our key innovation lies in enforcing causal invariance through dual consistency constraints: global causal isomorphism ensures the imputed variables preserve the ground-truth causal graph structure of the complete system, while local causal subgraph alignment maintains consistency between observed variables and their causal neighborhood dependencies. By decoupling causality from spurious correlations, GIMCC provides time-invariant imputation signals robust to distribution shifts, which explicitly preserves causal relationships via multivariate spectral convolutions. Extensive experiments across five real-world domains demonstrate that GIMCC achieves average improvements of 20-60% in MAE/RMSE over correlation-based imputation baselines, remarkably outperforming full-variable training ( Oracle ) in temporal covariate shift scenarios. Our work bridges the critical gap between causal analysis and practical forecasting systems under variable absence, offering theoretically grounded guarantees for real-world deployment.

Multivariate time series forecasting in practical deployment faces a critical challenge termed Variable Subset Forecasting (VSF), where certain variables accessible during training are entirely missing during inference. This creates a stark discrepancy between the training (source domain with full variables) and inference (target domain with partial variables) environments, disrupting cross-variable dependencies and fragmenting global temporal patterns. Existing imputation methods, limited to transferring local knowledge (e.g., temporal neighbors or pairwise correlations), fail to capture essential global dynamics, leading to severe performance degradation under distribution shifts. To address these challenges, we redefine VSF as a cross-domain knowledge transfer problem and propose VIDA, a framework that systematically transfers Variable Invariant knowledge from complete to partial observations through Domain Adaptation. Key to our approach is (1) Global time-frequency joint representation learning, which encodes temporal dynamics via dilated convolutions and captures low-frequency spectral consistency using Fourier neural operators, and (2) Sinkhorn-regularized distribution alignment to bridge non-overlapping feature supports across domains via optimal transport. Unlike imputation-first methods, VIDA enforces task-driven consistency by jointly optimizing predictions on reconstructed and original data, ensuring the transferred knowledge directly enhances forecasting robustness. Extensive experiments across four real-world datasets show that VIDA outperforms state-of-the-art imputation methods by 25% on average with partially observed variables. This work establishes a new paradigm for variable-missing scenarios by unifying imputation and forecasting through principled knowledge transfer.

Variable Subset Forecasting (VSF) refers to a unique scenario in multivariate time series forecasting, where available variables in the inference phase are only a subset of the variables in the training phase. VSF presents significant challenges as the entire time series may be missing, and neither inter- nor intra-variable correlations persist. Such conditions impede the effectiveness of traditional imputation methods, primarily focusing on filling in individual missing data points. Inspired by the principle of feature engineering that not all variables contribute positively to forecasting, we proposeTask-OrientedImputation forVSF(TOI-VSF), a novel framework shifts the focus from accurate data recovery to directly support the downstream forecasting task. TOI-VSF incorporates a self-supervised imputation module, agnostic to the forecasting model, designed to fill in missing variables while preserving the vital characteristics and temporal patterns of time series data. Additionally, we implement a joint learning strategy for imputation and forecasting, ensuring that the imputation process is directly aligned with and beneficial to the forecasting objective. Extensive experiments across four datasets demonstrate the superiority of TOI-VSF, outperforming baseline methods by 15% on average.