Label-Free Combination of Zero-Shot Time-Series Foundation Models

Zero-shot time-series foundation models (TSFMs) forecast unseen series without training, and since no single model dominates, practitioners pool several. On a new domain, however, no target label is available to decide how to combine them or which of them to include. We argue that both decisions follow from one observation, that without labels a member's error can only be contained, not corrected. Averaging distributions rather than quantiles contains it, and on 97 GIFT-Eval and 98 TIME configurations the quantile mean trails the linear opinion pool (LOP) on nearly all 120 subsets of seven TSFMs, while the best setting of every other rule family lands within half a percent of LOP. Which members enter the pool matters far more, yet a subset chosen in advance, even with labels from other sources, recovers only part of the gain of choosing with the target's labels, so selection has to happen inside the combination, one forecast at a time. We propose HuberLOP, which replaces the equal weights of LOP with Huber weights computed from each member's distance to a robust center of the pool. It improves on LOP on both benchmarks, and when three naive forecasters join the pool its conservative variant degrades by 0.9% on both benchmarks, where LOP degrades by 14.0% on GIFT-Eval and 12.0% on TIME. With no training and one threshold, it is a simple yet effective baseline for label-free TSFM combination. Code is available at https://anonymous.4open.science/r/ICLR27-TSFM.