Foundation Model Forecasts: Form and Function

TL;DR

This paper examines the types of forecasts produced by time-series foundation models, highlighting how forecast form impacts operational utility and establishing when different forecast types can be converted or are inherently distinct.

Contribution

It provides a comprehensive survey of TSFMs, formalizes conditions for forecast type conversions, and maps forecasting tasks to appropriate forecast forms for practical utility.

Findings

Two-thirds of TSFMs produce only point or parametric forecasts.

Trajectory ensembles can be converted to simpler forms via marginalization.

Marginal forecasts cannot determine path-dependent event probabilities.

Abstract

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.