When Correlation Is Not Enough: Utility-Driven Variable Routing for Time Series Forecasting

Multivariate time-series forecasting commonly models variable dependencies through statistical correlations. However, correlation does not necessarily translate into predictive gains, and fixed relationships cannot readily adapt to changing system states. To address these limitations, we propose TimeSpur, a time-dependent sparse predictive-utility routing framework. TimeSpur first establishes a stable independent forecasting basis from each variable’s own history and then constructs a sparse directed candidate graph using lagged relationships estimated from the training data. During training, paired stochastic masking measures the conditional predictive utility of a source variable for all targets against the observed future and uses this signal to calibrate a state-aware router. The model activates only candidate edges with positive utility under the current state and incorporates the resulting cross-variable information into the base prediction as a sparse residual. A single masking operation provides supervision from one source to all targets, avoiding exhaustive variable-wise evaluation in high-dimensional data. At inference, TimeSpur relies solely on the observed history, requiring neither masking nor future observations. Experiments on eight benchmark datasets demonstrate that TimeSpur achieves stable and competitive forecasting performance while controlling computational overhead.