Rethinking Cross-Channel Importance in Time-Series Forecasting

Abstract:Cross-channel modeling is central to multivariate time-series forecasting, yet channels that are statistically related, predictively useful, and actually used by a trained forecaster are often treated as if they defined the same notion of importance. We show that they need not coincide. Cross-channel dependency structures change substantially across future offsets, and horizon-adaptive source selection improves a controlled Ridge predictor in 21 of 32 dataset--prediction-length conditions, with a mean gain of $5.16\%$. This selected-set signal also transfers to a matched nonlinear predictor. Yet imposing the same horizon-specific source logic on iTransformer yields only 11 of 20 wins and a mean gain of $0.208\%$, with little alignment between controlled and neural gains. Functional interventions further show that strong forecasters use cross-channel information, while their source-reliance rankings agree little with controlled utility or with one another across iTransformer, TimesNet, and a cross-channel TimeMixer. As a constructive consequence, bounded post-hoc support improves a frozen channel-independent forecaster in 12 of 16 dataset--horizon conditions, with a positive aggregate bootstrap interval. Cross-channel importance should therefore be interpreted relative to the forecasting mechanism and question that define it: related $\neq$ useful $\neq$ used.

Machine Learning (cs.LG); Information Retrieval (cs.IR)

arXiv:2609.32187 [cs.LG]

(or arXiv:2609.32187v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32187 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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