Diagnosing Cross-Variate Access in Time Series Forecasting: Benefits, Edge Redundancy, and Allocation

Multivariate time-series forecasting is often framed through channel-independent or channel-dependent architectures, but this model-level distinction does not reveal which variables and forecast objectives benefit from cross-variate access, or what connectivity preserves those benefits. We introduce a controlled diagnostic framework using binary structural masks fixed throughout training and paired retraining to distinguish access benefit, budget sufficiency, and connection allocation. With input and prediction lengths both fixed at 96, we conduct primary experiments on four benchmarks using a compact iTransformer. We find that access benefits vary across datasets, receiving variables, and forecast objectives: aggregate noninferiority after removing cross-variate access can coexist with increased error for individual variables. After separately optimizing Short (steps 1–48) and Far (steps 49–96), we find stronger Short access benefits on Solar and ECL with both compact iTransformer and SAMformer. Positive access benefits also coexist with substantial edge redundancy: on Solar and ECL with compact iTransformer, randomly removing 90% of direct cross-variate edges satisfies a prespecified 1% noninferiority criterion for joint-96 mean squared error. Exploratory Solar sparsity curves further show sharply increasing Short error under extreme sparsification, while Far error remains close to the fully connected baseline. Beyond edge count, allocation also affects performance: at fixed budgets, restoring cross-variate coverage consistently reduces local error for previously isolated receivers across three real-data settings. In controlled synthetic experiments, connections to predictive-parent proxies outperform non-parent controls matched in edge count, receiver degree, and coverage. These findings support evaluating cross-variate interaction jointly in terms of forecast objectives, connection budgets, and allocation, providing empirical guidance for selective interaction mechanisms.