When Time Series Foundation Models Fail Under Cross-Channel Dependence

Multivariate time series foundation models (TSFMs) can access related series and covariates, but whether their forecasts reliably reflect the predictive value of cross-channel information remains unclear. We examine how Chronos-2, TimesFM-3, and TiRex-2 use cross-channel information through controlled synthetic experiments and real-world forecasting tasks. Our analysis covers cross-channel temporal relationships, dependence structures among observed channels, and the effects of known-future conditioning and covariate reliability. Useful cross-channel relationships are not consistently reflected in forecasts, while redundant or conditionally irrelevant inputs can still influence predictions. Statistical baselines fitted to the same observed contexts recover the relationships that the models underuse, indicating that these shortfalls reflect limited use of available information rather than its absence. On real-world tasks, conditioning on each model’s own median covariate forecasts increases quantile loss and reduces interval coverage. Propagating covariate uncertainty recovers much of this loss, but not all. Together, these findings reveal model-dependent limitations in exploiting temporal dependencies, combining information across channels, and producing reliable forecasts under covariate uncertainty.