Do Time-Series Foundation Models Preserve the Arrow of Time? A Surrogate-Gated Audit of Generative Time-Series Rollouts

Generative time-series models are usually evaluated by accuracy, calibration, or distributional fit, not by whether their sampled trajectories preserve the temporal direction of the process they model. We introduce a directional-retention audit for this question. A signed ordinal current, which reverses sign under time reversal, summarizes finite-window temporal asymmetry in observed and generated futures. Before any model comparison, Fourier surrogates test whether the observed current is distinguishable from a reversible null, and only supported currents serve as references. Generated currents are then compared with the observed one through relative magnitude $M$, directional cosine $C$, and signed projection $S=MC$. On hourly traffic panels from five cities, observed traffic shows supported directionality in three, whereas none of the 24-hour seasonal residuals does; the detected direction therefore reflects the daily traffic profile rather than a residual arrow after seasonal adjustment. In these three cities, Chronos-T5-tiny closely preserves the observed direction ($C=0.974$–$0.999$), while its signed projection ($S=0.80$–$1.11$) varies mainly through magnitude. Directional retention thus offers a path-level diagnostic of generated dynamics that complements conventional forecast metrics.