The Knowable Future
Definitions
The core vocabulary of forecastability. These definitions are stable and permanently anchor-linked for citation.
Forecastability. The amount of predictive information the observed past of a process carries about its future at a given horizon. It is a property of the series and the horizon, not of any model. High forecastability means the future is substantially knowable from the past; low forecastability means it is not, whatever method is applied.
Formal definition: Catt, P.M. (2026). Forecastability: a formal definition (version 1.0). Zenodo. https://doi.org/10.5281/zenodo.23031694
Forecastability profile, F(h). The function mapping each forecast horizon h to the predictive information available at that horizon from a declared information set. The profile is the complete, model-independent statement of how knowable a series’ future is, and the ceiling against which any method’s performance should be read.
Declared information set. The observations a forecast is allowed to use, specified before anything is measured. In plain terms: what was known, and when it was known. A declaration specifies the variables available, their timing and the history window. The variables may be the target’s own history alone, or may add other observed series such as price, weather or promotions. Everything in the set must be available at the forecast origin, the moment the forecast is made.
Exploitability. The predictive information a forecasting method attains from a declared information set for a specified target and horizon. Under logarithmic loss, expected attained information is measured in the same units as F(h) and is bounded above by F(h).
The exploitability ceiling. The limit F(h) places, at each horizon, on the expected predictive information attainable by any forecasting method using the same declared information set. The limit is exact under logarithmic loss. Estimates of either the ceiling or attained information carry sampling and estimation uncertainty.
Exploitability gap. The distance between the ceiling and a method’s exploitability at a given horizon: information that was available and went unexploited. The gap is the honest measure of forecasting performance.
Exploitability ratio. Exploitability as a share of the ceiling: the fraction of available predictive information a method converts into realised performance, comparable across series, horizons and methods.
Entropy. The information-theoretic measure of uncertainty: the average information required to specify an outcome. It is maximal for pure noise, lower wherever structure constrains what happens next, and the baseline a forecast is trying to reduce.
Auto-mutual information (AMI). Mutual information between values of the same series at different times. Lag-pair AMI compares the series with a single lagged copy of itself, so it is a diagnostic for a restricted information set and need not capture all the information in a longer history or in additional variables. AMI is a measure. It has to be estimated, for example by nearest-neighbour methods, and the estimator is stated separately.
Predictive information decay. The characteristic decline of F(h) as the horizon lengthens. Decay rates differ across processes and domains, which is why the same method can excel at one horizon and fail at another.
Forecast triage. The allocation of modelling effort informed by measured forecastability. Forecastability shows how much predictive information is available. Exploitability shows how much of it a forecasting method attains. Decision value determines whether closing the remaining gap matters in practice.
Predictive decision authority. The principle that the operational authority granted to a predictive system should scale with the forecastability of its domain. Systems forecasting weakly knowable processes should advise; only systems forecasting strongly knowable processes should act.
Cite this page: Catt, P.M. (2026). Definitions. The Knowable Future. theknowablefuture.com/definitions
For the formal statement, with notation and references, please cite the technical note: https://doi.org/10.5281/zenodo.23031694