Forecastability as an Information-Theoretic Limit on Prediction
Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the future observation and the declared information set equals the maximum achievable reduction in expected loss. This paper develops the consequences of that identity. Forecastability, defined as this mutual information evaluated across horizons, forms a profile whose shape reflects the dependence structure of the process and need not be monotone. Three structural properties are derived: compression of the information set can only reduce forecastability; the g...
| Authors | Peter Maurice Catt |
|---|---|
| Primary category | stat.AP |
| Published | 28 March 2026 |
| Last updated at source | 28 March 2026 |
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