Methodology

The question

Which model should forecast the next observation of a stream? That question needs the one-step metric isolated. Suites that pool steps 1 to H into one score cannot answer it, and a model that is strong at step one and ordinary after is indistinguishable there from one that is flat.

The protocol

Every model forecasts the one-step change of a series from a fixed context, rolling over a test window; every forecast becomes a full predictive density scored by log likelihood and CRPS at the realised value. Pretrained models run zero-shot, each in its own environment, on CPU. Their quantile outputs are turned into densities by a stated reconstruction: native levels where the model emits them (21 for Timestral and t0-gamma), the generous bandwidth otherwise, because a tight reconstruction of nine deciles manufactures about half a nat of apparent deficit.

Pairing and the test

Every model is paired against laplace, the training-free online yardstick, on identical series and windows. Per series the mean log-score differential is tested by Diebold–Mariano with a Newey–West standard error; a win or a loss is a difference beyond 1.96 standard errors, the rest are draws. A draw says the window cannot separate the two, not that they are equal, so the median gap is the better measure of size.

Baselines that keep learning

The classical baselines in published suites are fit once at the window origin and never updated. Here every baseline is online: it sees every observation before it forecasts the next. The gap between foundation models and classical methods shown here is therefore the gap a practitioner running a stream would see. AutoARIMA, AutoETS, AutoTheta and GARCH-t are refit at every step.

Trained models

laplace++ is the one trained model here. It is trained on half of each panel, split by series family, and every number shown for it is on the other half. Training data added from outside the panel is never one of the held-out series. How it is built and what it guarantees are on the laplace++ page.

Roster

Only the best models in each class, each with public code and a pinned checkpoint that was run here. Submissions that cannot be rerun are not listed.

Licences and versions

The licence column gives each model's terms. Of the seven foundation models, three are open, two are free below a revenue threshold, and TimesFM 3.0 and TimeH2O are licensed for testing, evaluation and research only. laplace, laplace++ and the classical models are open. All evaluation here is non-commercial benchmarking. TimeH2O is h2oai/timeh2o-v1 at Hugging Face revision c556990, whose weights are unchanged since revision 60b68fa of 2026-10-22, run zero-shot on CPU on 2026-11-03 and 2026-11-04 by the protocol above.

Source

The tables are generated from the skaters repository's committed summaries, the per-step store behind them, its cost measurements and its footprint measurements, by build.py in this repository. The same files drive skaters.microprediction.org, which carries the per-model pages, the sandwich results and the papers.