MarCO: Propagating Covariate Uncertainty for Time Series Forecasting with Exogenous Variables

Exogenous variables (i.e., covariates) often govern how a target time series evolves: electricity prices follow load and renewable generation, and wind power follows wind speed. Existing methods either forecast deterministically, encoding historical covariates as features or forecasting the covariates first and using that single trajectory, or forecast the target probabilistically while treating the covariates as fixed context. Neither models the future covariates, which are unknown when a forecast is issued, probabilistically, nor captures how their individual uncertainties combine into a joint distribution over covariate futures to which the target should respond. We propose MarCO, which treats the future covariates as a random vector: it forecasts their marginal distributions, couples the marginals into a joint distribution through a copula, draws coherent covariate scenarios from it, and lets every scenario modulate the target forecast, which is obtained as the mixture over scenarios. Using historical inputs only, MarCO ranks first in MSE on 11 of 12 real-world datasets against state-of-the-art deterministic and probabilistic methods and reduces their average MSE by 5.2% and 5.9%, while additionally quantifying the uncertainty of the covariates themselves.