Papers
Papers built on the skaters library. Sources and run logs are in the papers/ and benchmarks/ directories of the repository. The benchmark studies themselves live on the benchmarks page.
Transforms all the way down: automatic online distributional forecasting by conjugation
The methods paper. Every prediction is a full predictive distribution, assembled by composition: invertible transforms chain onto a single distributional leaf fitted by a proper scoring rule, and the collection collapses into one forecast function with no exposed tuning parameters. It leads the held-out log-likelihood race against classical, neural, and foundation-model baselines on FRED series, with the asset-price split reported rather than averaged away. Written twice, in pure Python and zero-dependency JavaScript, held to 1e-6 agreement by a parity suite.
An empirical study of the conformal information gap
The companion study, with skaters as the measurement instrument. Under logarithmic loss the irreducible cost of a retained representation is a conditional mutual information, the information gap. A nested ladder of transforms prices each representation family prequentially on 701 economic series: conditional scale is the largest and most reliable component of the gain, and scale-normalized empirical pooling beats raw pooling on 87 percent of series under CRPS.
PDF experiment scripts SSRN preprint, 2026; under journal review
skaters: online distributional time-series forecasting by conjugation, in Python and JavaScript
The short software paper describing the package itself: the transform contract, the conjugation recursion, the parity-locked ports, and the calibration state that turns the forecaster into an anomaly detector.
paper.md under review at the Journal of Open Source Software
Citation
@misc{cotton2026skaters,
title = {Transforms All the Way Down --- Automatic Online Distributional
Forecasting by Conjugation},
author = {Cotton, Peter},
year = {2026},
note = {https://skaters.microprediction.org}
}