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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Ceiling Holds, and So Does Climatology: Loss Functions and Calibrated Uncertainty Against an Empirically Measured Predictability Limit

Authors: Ramanathan, Arun;

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

Abstract

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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