Foundation Model Forecasts: Form and Function
This work addresses the practical utility gap in forecasting for operational decision-makers, though it is incremental in mapping tasks to forecast types.
The paper tackles the problem that time-series foundation models often produce forecast types (e.g., point or parametric) that are insufficient for many operational tasks requiring trajectory ensembles, and it establishes conversion limitations and provides a task-aligned evaluation framework.
Time-series foundation models (TSFMs) achieve strong forecast accuracy, yet accuracy alone does not determine practical value. The form of a forecast -- point, quantile, parametric, or trajectory ensemble -- fundamentally constrains which operational tasks it can support. We survey recent TSFMs and find that two-thirds produce only point or parametric forecasts, while many operational tasks require trajectory ensembles that preserve temporal dependence. We establish when forecast types can be converted and when they cannot: trajectory ensembles convert to simpler forms via marginalization without additional assumptions, but the reverse requires imposing temporal dependence through copulas or conformal methods. We prove that marginals cannot determine path-dependent event probabilities -- infinitely many joint distributions share identical marginals but yield different answers to operational questions. We map six fundamental forecasting tasks to minimal sufficient forecast types and provide a task-aligned evaluation framework. Our analysis clarifies when forecast type, not accuracy, differentiates practical utility.