Abstract

Machine learning systems increasingly inform decisions whose consequences unfold across multiple temporal horizons, from short-term operational control to long-term strategic planning. Despite substantial progress in probabilistic forecasting and uncertainty quantification, prevailing approaches largely treat uncertainty as horizon specific, implicitly assuming that forecast errors remain local to the time step at which they arise. This assumption is theoretically fragile and empirically misleading in settings where predictions recursively shape downstream decisions and future data-generating processes. This paper develops a unified analytical framework for uncertainty propagation in multi-horizon machine learning systems. Drawing on Bayesian decision theory and stochastic systems theory, we conceptualize multi-horizon prediction as a coupled stochastic process in which epistemic and aleatory uncertainty evolve endogenously through decision feedback loops. We formally characterize propagation mechanisms, derive conditions under which uncertainty amplifies nonlinearly over time, and demonstrate how short-horizon calibration can coexist with long-horizon overconfidence. The framework is illustrated using empirically grounded scenarios drawn from healthcare operations, energy demand planning, and retail inventory management. Across contexts, ignoring uncertainty propagation leads to systematically distorted beliefs and suboptimal decisions. The contribution advances theory by reframing multi-horizon machine learning as a dynamic uncertainty system, introduces a methodological apparatus for tracing uncertainty flow across horizons, and clarifies managerial and policy implications for high-stakes decision environments. The results provide a foundation for more credible, auditable, and resilient machine learning systems.