Report the Floor: A Training-Free Conformal Interval Is a Mandatory Baseline for Probabilistic Time-Series Forecasting

Probabilistic forecasters are increasingly learned, yet the baselines they are compared

against are often weak or omitted. We show that the simplest possible conformal interval

— a last-value point forecast wrapped in a finite-sample split-conformal residual quantile,

with no parameters and no training — is a far stronger baseline than its near-total absence

from recent learned-forecasting and conformal–time-series comparisons would suggest.

In one-step-ahead online forecasting across 2,217 real series spanning nine public sources

(the Monash archive, the LOTSA collection, the LTSF traffic/electricity/weather suites,

METR-LA, BOOM, and nips/probts), this ConformalNaive interval decisively beats the

naive value-quantile baselines, the entire NPTS family (NPTS 73%, SeasonalNPTS 64% of

series), and the published Conformal Seasonal Pools (CSP) method (71% of series, bootstrap

95% CI [69, 73], p ≈ 7.6 °ø 10−135); it is on par with the simpler learned conformal

predictors (RCI, quantile regression; median relative Winkler within 2%) and is beaten only

by the adaptive-online and ensemble conformal methods (SPCI, ACI, AgACI), which explicitly

track distribution shift and lead by 9–33% relative Winkler. It is also better calibrated

than a trained neural forecaster: on the six datasets that introduced DeepNPTS, the trivial

conformal floors cover the truth 84–85% of the time at a nominal 95%, versus DeepNPTS’s

66%. At multi-step seasonal horizons the picture inverts: the random-walk floor is the

weakest method and the seasonal pool (CSP) wins — a boundary we map so practitioners

know when complexity is actually required. Finally we give ConformalNaive+, a one-line,

training-free, horizon-adaptive selector that attains the better of two complementary floors

at every horizon with restored coverage. We argue the matching conformal naive floor must

be a mandatory baseline whenever a learned probabilistic forecaster claims gains.