Timestral vs Laplace

Timestral is Mistral's zero-shot time-series model, released 15 October 2026 in four sizes; it emits 21 non-crossing quantiles per step, from the 1st to the 99th percentile. Run zero-shot on CPU with a fixed 128-length context, symmetric averaging and the nonnegativity clip switched off (the series are signed changes). The headline row is the 209M checkpoint scored on all 21 native levels; the other sizes and the nine-decile reconstruction are tabled below.

Resources: GitHub · Model card

This page measures one thing: how sharp and how well calibrated Timestral's univariate predictive density is, one step ahead on a change series, scored against Laplace on identical windows. It leaves out the covariates, the multivariate inputs, the long horizons and the native quantile or path outputs the model was built for, and its log score passes through a reconstruction of the model's quantiles (the table note says which). A model can trail here and be the better tool for its own job.

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. Win, draw and loss are decided one series at a time. Each series has a rolling test window of 64 one-step-ahead points, and both forecasters are scored on the same points. For each point take the difference of log predictive densities, dt = log pmodel(yt) − log pLaplace(yt), with each log density floored at −20 first. The series' mean d̄ is tested against zero by a Diebold–Mariano test: the standard error is Newey–West with a Bartlett kernel and lag round(n^1/3). The model wins the series if d̄ > 1.96·SE, loses it if d̄ < −1.96·SE, and otherwise the series is a draw; a series with fewer than eight finite differences is a draw. A draw says the 64 points cannot separate the two forecasters at the 5% level. It does not say they are equal. With a window this short both win and loss counts understate the true rates, and the median ΔLL is the better measure of size. Counts are over the series both arms cover.

On the model's native 21 quantile levels

Arm Timestral-209M(q21): the model's own 1% to 99% quantiles through the fixed-bandwidth reconstruction, with no bandwidth inflation. The tails are the model's. This is the fairest density the model can be given, so it is the headline.

Median per-series Δ log-likelihood in nats (negative is worse than Laplace); CRPS ratio to Laplace (above 1 is worse); central-90% coverage (0.90 target). Coverage is that of the reconstruction on the native 21 levels; fed a calibrated normal's quantiles it covers about 0.89, so a perfectly calibrated model reads 0.89 here.

Tight nine-decile reconstruction

Arm Timestral-209M: the same forecasts through quantile_dist, the reconstruction the original study used. Fed the exact deciles of a standard normal it covers 0.81, so a perfectly calibrated model reads 0.81 in this coverage column and pays for it in log score. It understates the model and is kept here for comparison with the earlier numbers.

Median per-series Δ log-likelihood in nats (negative is worse than Laplace); CRPS ratio to Laplace (above 1 is worse); central-90% coverage (0.90 target).

Checkpoints and level sets

The same model family scored several ways on the identical windows. Each cell is the median per-series Δ log-likelihood in nats against Laplace (negative is worse), with the reconstructed central-90% coverage in parentheses (0.90 target). The nine-decile rows use the same fixed-bandwidth reconstruction as TiRex-2; the 21-level rows feed the model's native 1% to 99% quantiles to that reconstruction. The model is the same in both blocks; only the reconstruction differs.

Star plot

Timestral standalone against Laplace, on the same six regime axes as the site's standalone radar. Each radius is the log-likelihood win rate, (wins + ½·ties) / n, divided by one half so an even split with Laplace sits on the dashed 1.0 ring; outward beats Laplace more often, inward less. The quantity is a share of series. The solid polygon is the headline arm and the dashed grey one, where present, is the tight nine-decile reconstruction. The M4-hourly set splits into soft and hard waveforms by corpus order, matching that radar.

Collaborative use

The recalibration (@lap) and portfolio (&lap) arms were built for the three strongest models first, so Timestral is scored standalone here. The sidecar wraps any per-step predictive, so these arms can be added without retraining. See the sidecar pattern.

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

Timestral is a patched transformer with an hourglass encoder, trained to emit 21 quantile levels per step with a context of up to 32,768 points and support for covariates and multiple variates, none of which this univariate study uses. Its 1% and 99% quantiles are native outputs, so its density needs no bandwidth inflation to carry tails. Scored on all 21 levels, the 123M and 209M are ahead of Laplace at the median on weekly, monthly and M4-hourly series, level on price, and a few hundredths behind on daily econ, with the same coverage as Laplace. On the nine deciles alone it reads like every other quantile model, about half a nat behind. Pretraining contamination is unchecked.