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 gap between the profile under a finite lag window and the full history gives an exact truncation error budget; and for processes with periodic dependence, the profile inherits the periodicity. Predictive loss decomposes into an irreducible component fixed by the information structure and an approximation component attributable to the method; their ratio defines the exploitation ratio, a normalised diagnostic for method adequacy. The exact equality is specific to log loss, but when forecastability is near zero, classical inequalities imply that no method under any loss can materially improve on the unconditional baseline. The framework provides a theoretical foundation for assessing, prior to any modelling, whether the declared information set contains sufficient predictive information at the horizon of interest.

翻译：预测通常被建模为模型选择问题。本文从更根本的问题出发：在每个预测时域上，究竟有多少预测信息可用？在对数损失函数下，答案具有精确性：未来观测与已知信息集之间的互信息等于预期损失的最大可降低量。本文发展了该恒等式的理论后果。所谓“预测可衡量性”（定义为此互信息在不同时域上的函数），其曲线形态反映了过程的依赖结构，且不必是单调的。本文推导出三个结构性质：信息集压缩会降低预测可衡量性；有限滞后窗口下的曲线与完整历史曲线之间的间隙给出了精确的截断误差预算；对于具有周期依赖性的过程，该曲线继承其周期特性。预测损失可分解为两部分：由信息结构决定的不可约分量，和由方法选择导致的近似分量；两者之比定义了“利用率”，一种用于评估方法充分性的归一化诊断指标。该精确等式仅在对数损失下成立，但当预测可衡量性接近零时，经典不等式表明：在任何损失函数下，任何方法都无法实质性改进无条件基线模型。该框架为在建模之前评估指定信息集在目标时域上是否包含足够预测信息提供了理论基础。