Causal-Guided Ultra-Long-Term Time Series Forecasting Via Anticipated Covariates

Time series forecasting aims to discern latent patterns and predict future states. The incorporation of covariates, such as seasonal information, has effectively improved medium- to long-term forecasting accuracy by capturing cyclical trends. However, the gradual accumulation of errors continues to constrain performance over ultra-long horizons. Often treated as unknown, information from the future remains underutilized. In this work, we demonstrate that in a coupled dynamical system, providing the future state of the effect $X$ enables accurate forecasting of the cause $Y$ for thousands of timesteps. The forecasting error remains bounded even in the presence of an unobserved variable $Z$ driving the target (i.e., $Z\to Y\to X$ ), confirming that future effect information inherently stabilizes and guides the trajectory of present causes. In light of this, we propose a time series forecasting paradigm that introduces anticipated covariates to represent such known future states. We validate this finding across several widely adopted benchmarks. Under suitable conditions, ultra-long-term predictions become feasible with forecast errors substantially reduced. We expect the anticipated covariates paradigm to be a powerful tool for situations constrained by high data costs, limited historical data, or unobservable causal factors, and to prompt a re-evaluation of reverse time-dependent causality.