PRISM: Interpreting Time-series Foundation Models via Zero-shot Basis Decoding

Time-series foundation models (TSFMs) generalize across diverse domains, enabling zero-shot forecasting. However, their forecasts do not explicitly identify the contribution of trends and periodic patterns, even though interpretation is a central objective of classical time-series analysis. We introduce PRISM, which decodes a frozen TSFM’s representation of the observed context into an additive forecast, fitting nothing to the target series. PRISM predicts a piecewise-linear trend, gates and weights a Fourier dictionary restricted to the periods the sampling interval and horizon admit, and adds a residual contribution, so that the forecast is a sum of components that can be inspected one at a time. On TimesFM 2.5, the components reproduce the calendar and physical structure that domain knowledge predicts in three domains, and where a cycle is present the seasonal components agree with a consensus of classical decompositions of the realized future. Where no cycle exists, as in exchange rates, the seasonal component stays near zero while the decomposers still report one. On strongly seasonal series under input noise, it revises less than the same bases fitted to the backbone’s forecast. Among component-wise forecasters, Ours has the lowest error on three of five dataset groups, with dataset-averaged MAE/σ 7.15% above the frozen backbone.