skaters (demo,docs)

A light, accurate, autonomous distributional forecaster for non-price economic series in particular. Watch here.

Laplace beats (almost) everything.

And it beats them across nearly every regime, giving ground only on price/returns (to GARCH-t) and, narrowly, on the hard, repeating waveforms (to CSP¹).

Laplace is fast, dependency-free, online univariate distributional forecasting with parity-locked ports in Python, JavaScript, R, Julia and Rust (all matched to the reference within 1e-6; JavaScript and Pyodide run it in the browser). It's a general-purpose forecaster for non-price economic series. On FRED change-series scored one step ahead, it beats AutoARIMA, AutoETS, AutoTheta, GARCH-t and NPTS on held-out log score at every frequency, and on 2,179 daily series it beats every zero-shot foundation model tested. On 5,576 monthly series the newest foundation models (Timestral-209M, TimeH2O, TimesFM 3.0, t0-gamma) are ahead, by 0.05 to 0.10 nats per step at the median, and on 3,013 weekly series three of the four are. On price and return series laplace, GARCH-t and the foundation models are level. Every foundation-model figure depends on how its quantiles are turned into a density (see the benchmark paper).

Not for price/return series: We recommend GARCH-t there instead.

When CRPS is the target: A scoring rule is a settlement rule — match it to what you actually want. skaters defaults to held-out log-likelihood because it ranks reusable densities, and on CRPS laplace still beats most of the competition. But if your target really is CDF shape or threshold behaviour, CRPS is a reasonable contract and a method like conformal prediction may suit — just know it is a different contract, not a better density. (Why skaters ranks by likelihood, by default →)

Install

pip install skaters

Quick start

from skaters import laplace

f = laplace(k=3)
state = None
forecast = None            # the fan issued LAST tick, aimed at this y
for y in observations:
    if forecast is not None:
        forecast[0].logpdf(y)          # one-step-ahead log score
        forecast[0].cdf(y)             # one-step-ahead PIT
    forecast, state = f(y, state)
    forecast[0].mean                   # point forecast for the NEXT tick
    forecast[0].std                    # uncertainty
    forecast[0].quantile(0.975)        # upper edge of the central 95% band

Score a forecast only against observations that arrive after it was issued; the predictive returned alongside y aims at the next tick, and the parade in state["pit"]/state["z"] does this bookkeeping for you. Every skater returns a list of predictive distributions, one for each horizon $h = 1, \ldots, k$. Point forecasts, uncertainty, density evaluation, and quantiles are all aspects of the same object.

laplace — the general forecaster

skaters exposes exactly one forecaster, laplace. Everything else is a building block (transforms, leaves, ensembles) you can compose. ("skater" is the concept — any (y, state) -> ([Dist], state) function, borrowed from the old timemachines package.) At multi-step horizons (k>1) it is multi-scale by default (below).

from skaters import laplace

f = laplace(k=1)

A likelihood-weighted Bayesian ensemble over a large candidate population (EMA, differencing, drift, Holt, AR, fractional differencing, seasonal, a Yeo-Johnson coordinate grid, a fast/slow two-systems block, and — at multi-step horizons (k>1) — an Ornstein–Uhlenbeck mean-reversion group). Three things are on by default, each a free or near-free win:

• model first, score-optimize last — the trunk is weighted by likelihood; the terminal leaf is fit by CRPS (objective="crps"). On a 2,500-series FRED study this matches a CRPS specialist on CRPS and lifts likelihood on real data. Switch back with objective="likelihood".
• lattice projection (sticky=True) — near-Dirac atoms on the exact values a series revisits. Free on continuous data (it vanishes), a large win on grid/repeating series (policy rates, posted prices).
• coordinate learning — a Yeo-Johnson λ-grid lets the ensemble learn whether the series is simple in a log/multiplicative, sqrt, or linear coordinate.

f = laplace(k=1)                          # CRPS leaf + lattice, both on
f = laplace(k=1, objective="likelihood")  # pure-likelihood leaf
f = laplace(k=1, sticky=False)            # no lattice projection

Calibration state, free. Every arriving point is resolved against the forecasts previously made for it: state["pit"][m-1] is its probability integral transform under the m-step-ahead predictive issued m steps ago (roughly Uniform(0,1) when calibrated) and state["z"][m-1] the same through the standard-normal quantile (roughly N(0,1); z is clamped to ±7.03, never infinite). That calibrated-surprise signal is the null model streaming anomaly detection is built on, and that work lives in its own project: timemachines — calibrated online anomaly detection with honest false-alarm rates, built on skaters.

Footnotes

1. On the hard-waveform arm (near-deterministic, repeating cycles) CSP is handed the seasonal period, while laplace is not and must infer structure generically. Its edge there reflects that head start, not a like-for-like loss. ↩

以上為 README 的開頭部分。其餘內容請閱讀原文。 檢視完整 README ↗