When Does Forecasting Reveal Temporal Structure? Recoverability and Stability of Forecast-only Explanations

Forecast accuracy is often used as a proxy for temporal structure discovery, but predictive performance and structural recoverability are not equivalent. Forecast-only structural selection—choosing among candidate temporal structures based solely on their forecasting performance—provides a practical way to identify predictive temporal dependencies for model interpretation, diagnosis, and downstream decision making. 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 relates reliable forecast-only structural selection to the margin's robustness against uncertainty in the selection objective. Experiments across controlled and end-to-end settings demonstrate that forecast margin alone is insufficient, while the proposed stability condition provides a sufficient guarantee for correct forecast-only structural selection. We further give a model-based certification procedure that uses independent data to check the selected structure under a declared structural family, abstains when the evidence is insufficient, and does not require knowing the candidates' ideal risks. Our results suggest that predictive accuracy can support structural interpretation when its advantage is sufficiently robust, or when the selected structure is independently certified under a declared structural family. More broadly, our framework provides a principled basis for evaluating when forecast-derived temporal structures can be trusted as model explanations in theoretical analysis and finite-candidate time-series applications.