Chronos vs Laplace
Chronos tokenizes a series into a fixed vocabulary and forecasts it autoregressively, like a language model over quantized values. Reused from the earlier foundation study; run zero-shot on the one-step change series.
Resources: GitHub · Model card · Paper (arXiv 2403.07815)
Live snapshot Derived from the week-long round-robin study; counts grow as coverage deepens. Everything scores against Laplace on the identical series and windows.
Standalone
The model's own predictive, run zero-shot, scored per series against Laplace by a one-step-ahead (k=1) Diebold–Mariano test on the log-score differential.
| stratum | n | win / draw / loss vs Laplace | med ΔLL | CRPS ratio | cov₀₀ |
|---|---|---|---|---|---|
| economic change-series, business-daily | 1328 | -1.12 | 1.020 | 0.82 | |
| economic change-series, weekly | 2720 | -1.21 | 0.992 | 0.82 | |
| economic change-series, monthly (annual cycle) | 2720 | -0.86 | 0.977 | 0.79 | |
| M4 hourly, strongly seasonal | 414 | -0.52 | 1.016 | 0.84 | |
| asset prices and returns, daily | 1392 | -0.87 | 1.023 | 0.77 |
Median per-series Δ log-likelihood in nats (negative is worse than Laplace); CRPS ratio to Laplace (above 1 is worse); raw central-90% coverage (0.90 target).
Star plot
Chronos standalone against Laplace, on the same six regime axes as the site's
standalone radar. Each radius is the log-likelihood
ratio, (wins + ½·ties) / n scaled so an even split with
Laplace sits on the dashed 1.0 ring; outward beats Laplace more often, inward less. The
M4-hourly set splits into soft and hard waveforms by corpus order, matching that radar.
Collaborative use
Two collaborative arms wrap Chronos's own predictive. @lap
lets Laplace forecast the model's normal scores, which fixes coverage; &lap
holds Laplace and that wrap in a long-only online portfolio, so the blend is never
much worse than Laplace alone. The recalibration pulls raw coverage back toward the
0.90 target, and the portfolio collapses the loss rate against Laplace.
| stratum | raw cov | @lap cov | raw loss | &lap loss |
|---|---|---|---|---|
| economic change-series, business-daily | 0.82 | 0.92 | 67% | 31% |
| economic change-series, weekly | 0.82 | 0.90 | 58% | 15% |
| economic change-series, monthly (annual cycle) | 0.79 | 0.91 | 45% | 7% |
| M4 hourly, strongly seasonal | 0.84 | 0.92 | 39% | 1% |
| asset prices and returns, daily | 0.77 | 0.91 | 56% | 5% |
Central-90% coverage (0.90 target) and the fraction of series where the arm loses to Laplace by a Diebold–Mariano test.
Protocol
Fixed 128-length context, rolling one-step test window, no fitting, each model in its own environment. Strata split the cached FRED universe and the M4-hourly set by frequency and regime. Full method on the sidecar pattern page and in the methodology.
Architecture and methodology
Chronos treats forecasting as language modelling. It scales and quantises the series into a fixed token vocabulary, trains a T5-style transformer on the token sequences with a cross-entropy loss, and forecasts by sampling tokens. This study runs the Chronos-Bolt variant (chronos-bolt-small), which patches the context and emits quantiles directly in a single forward pass rather than sampling autoregressively; it is far faster, but its log-likelihood is a quantile reconstruction, so read its CRPS as the primary signal.