The Ceiling Holds, and So Does Climatology: Loss Functions and Calibrated Uncertainty Against an Empirically Measured Predictability Limit

A previous paper in this series found that no forecasting model — however sophisticated, however

much data it saw — could beat a hard, measurable limit on how far ahead a financial instrument’s

price can genuinely be predicted; every model just converged on a plain historical average. This

paper asks two further questions. First: does training a model to avoid a different kind of mistake

— getting rare, extreme outcomes right, or reporting a range instead of one number — change

that? No: the model still reports “about the same as usual,” or becomes unstable if pushed hard

enough to try. Second, and more interesting: what if a model stops giving one confident number

and instead honestly reports a whole range of plausible outcomes? We built a system that does

this, calibrated against how much prices have actually moved historically. Its central prediction is

mathematically identical to the plain average’s — it has not predicted the future any better. But

judged by a proper scoring rule that rewards being honestly right about uncertainty, it beats every

fancier model tested, as long as those models are forced to pretend they’re certain. Three of them,

though, are not actually certain internally, so we gave every model, including the plain average, its

own honest, unmodified shot at reporting uncertainty. Our carefully calibrated system still beats

every fancier model’s own honest uncertainty. But it does not always beat the plain historical

average’s own honest uncertainty — a simple, unprocessed sample of recent real prices, no

modeling at all — which wins outright more than half the time. The wall limiting how far ahead

markets can be predicted is still standing, untouched. Being honest about that wall, instead of

pretending it isn’t there, is itself something a model can get measurably right or wrong — and

even a carefully built system for it still competes with, and often loses to, simply telling the truth

using the real data already at hand.