Benchmarks

A new practical benchmark for univariate distributional prediction — simpler and lighter than Prophet, and scored where it counts: held-out likelihood.

Benchmark 1 — the non-price universe

A fair rolling one-step-ahead comparison on the non-price FRED universe — 894 continuous daily change-series (57 correlated families); equity/fx/commodity returns are excluded and treated separately in the price caveat below. Every method — ours and theirs — is turned into the same Dist and scored on held-out log-likelihood and CRPS. Per-series win-rate of laplace, reported raw and family-weighted (one vote per correlated family):

laplace (mean log-likelihood 3.20) wins the likelihood race against every baseline on non-price series — including GARCH-t, the heavy-tail SOTA (68% raw / 65% family-weighted; mean LL 3.20 vs 3.03). On CRPS it beats the mean-model baselines and loses only to the CRPS-specialists (fitted conformal ~30%, GARCH-t 45% family-weighted) — their home turf. No free lunch on price/returns: on equity/fx/commodity return series GARCH-t has the higher log-likelihood, and we recommend it there rather than averaging the two regimes into one number. The study →

Benchmark 2 — zero-shot foundation models

A different protocol: pretrained models used zero-shot (fixed 256-context, no refit) on 120 change-series (69 continuous). Per-series win-rate of laplace:

On the continuous series, laplace beats all four zero-shot. The native-density models (Moirai, Lag-Llama) are the closest. Naive per-series fine-tuning doesn't rescue them — it catastrophically overfits (logpdf +1.5 → −118). A zero-dependency online ensemble holding its own against 200M-parameter transformers. The foundation study →

Challengers

Every method that has stepped up, one row each with its tape, lives on its own page now, built for the ones still coming: Challengers.

Reproducibility

All studies are reproducible end-to-end from skaters/benchmarks. The papers behind them are on the papers page.