Are Time Series Foundation Models Statistical Model Selectors?

Automatic model selection is a routine, and costly, step in statistical forecasting practice. Procedures such as AutoETS and AutoARIMA choose from among a family of statistical model shapes by fitting and scoring each candidate against an in-sample criterion. In contrast, pretrained time series foundation models (TSFM) encode a series into a fixed-width representation in a single forward pass, at a small fraction of the cost of the search. In this paper, we present an early investigation into whether such representations already encode the model shape that a statistical model search would select, without running the search itself. We find that simple probes on TSFM representations recover the search's own model selection above baseline performance. Forecasting with the probed form is 3--13x faster than running the search. However, forecasting with the probed form leads to a contained but noticeable regression in forecasting accuracy. Our results indicate that TSFM representations carry the statistical structure a model search recovers, and can stand in for the search where a small loss in accuracy is acceptable.