When Does Forecasting Reveal Temporal Structure? A Stability Analysis of Time-Series Structural Selection

Abstract

Forecast accuracy is often used as a proxy for temporal structure discovery, but predictive performance and structural identifiability are not equivalent. Different temporal mechanisms can achieve similar forecast errors, while small forecast differences may still contain sufficient information for recovery. In this work, we study when forecast-only structural selection can be trusted. We show that a vanishing forecast margin does not necessarily imply structural ambiguity, and establish a stability perspective that evaluates structural separation relative to uncertainty in the selection objective. This perspective provides both a sufficient condition for reliable selection and a continuous measure of selection difficulty. Experiments across controlled and end-to-end settings demonstrate that forecast margin alone is insufficient, while the proposed stability measure better characterizes when forecast-based structural selection succeeds or fails. Our results suggest that predictive accuracy should be treated as evidence for structure discovery only when its separation is sufficiently robust.