Code
Alternatives
If the problem is a distributional forecast, wrap nothing: model the conditional distribution.
Conformal prediction certifies coverage. If what you need is a sharp conditional distribution, the workhorses below are where to start. Each buys sharpness with assumptions. Conformal buys assumption-freeness with marginality. Nobody escapes the trade. On the question of which method actually wins on which series, this page defers to the live skaters benchmarks; treat the notes below as orientation, not a ranking.
Caveat: these recommendations go stale
These recommendations are likely to be stale before long. This site is intended primarily as a list of mathematical insights; benchmarking is fluid, ongoing, and best found elsewhere. Open efforts worth checking: skaters.microprediction.org (autonomous, continuously running, distributional), the Monash forecasting repository, the M competitions (data and results are open), and GIFT-Eval for the zero-shot foundation models.
t-GARCH
The classical econometric route: conditional volatility with Student-t innovations. The standard choice for price and return series, where volatility clustering is the signal and heavy tails are the rule. The assumption purchased is that the GARCH recursion is roughly right; when it is not, the tails you paid for are the wrong ones.
auto-ARIMA
The workhorse baseline: search the ARIMA orders, fit by maximum likelihood, forecast with Gaussian innovations. Of the implementations, statsforecast’s AutoARIMA is the one that has held up in the skaters studies: fast enough to run everywhere and rarely far wrong, which is much of what an autonomous baseline is for. The assumption purchased is linearity with a fixed innovation shape: the point forecast is often serviceable while the interval inherits a constant-shape residual, so on heteroscedastic series it makes the same trade as the conformal wrapper, a level without a shape.
laplace
An online likelihood-weighted ensemble from the skaters package: one call, zero dependencies, a full predictive distribution per step. It has done well on non-price economic series in the skaters benchmarks, where the current standings live. The assumption purchased is that the recent past is informative enough for the ensemble to track; and it hands you no finite-sample coverage certificate.
pymc_forecast
The fully Bayesian route: pymc_forecast (PyMC Labs) has you write the generative model in PyMC and handles the rest — inference, forecasting, and rolling-origin backtesting with CRPS and coverage metrics. You get the whole posterior predictive, hierarchies included. The assumption purchased is the model itself, prior and likelihood: the intervals are credible, calibrated exactly to the extent the model is right, with no distribution-free certificate.
Waveform methods
Some series are repeated sampling in disguise: daily electricity load, where the right reference class for this morning’s 7am is the other 7am’s. NNS (Viole) forecasts by resampling those matched periods, and a training-free seasonal-pool conformal forecaster built on the same observation is already a strong baseline (Manokhin, 2026). Not the author’s specialty; the financial uses are somewhat niche. The wider point is the one to take: state-of-the-art prediction or anomaly detection in your domain comes from common sense about the structure of your series, not from a recipe. Matrix profiles, for instance, are a natural fit for medical time-series, where the event of interest is a repeated motif or its absence.
The trade
Any of them can be conformalized afterwards for the certificate: estimate first, certify second. Demo 17 and the worked example run the comparison, and the two-prices note prices what ignoring the conditional information costs. There is no free lunch: the conditional models pay in assumptions, conformal pays in sharpness, and the only real decision is which bill your application can afford.
NNS and the seasonal-pool idea both run live on the skaters benchmarks, part of an ongoing effort to learn whether one general-purpose autonomous forecaster can mostly match the specialists on waveform-like series without paying a steep price on economic ones. That question is a lesson that recurs across these pages: modeling is not automatic in general, and residual analysis, however much we would like it to be, is not automatic either.