Forecasting fails not because models are weak, but because effort is wasted on series whose futures are fundamentally unknowable. We propose a pre-modelling diagnostic framework that assesses horizon-specific forecastability before model selection begins, enabling practitioners to allocate effort where it can yield returns. We operationalise forecastability as auto-mutual information (AMI) at lag h, measuring the reduction in uncertainty about future values provided by the past. Using a k-nearest-neighbour estimator on training data only, we validate AMI against realised out-of-sample error (sMAPE) across 1,350 M4 series spanning six frequencies, with Seasonal Naive, ETS, and N-BEATS as probe models under a rolling-origin protocol. The central finding is that the AMI-sMAPE relationship is strongly frequency-conditional. For Weekly, Hourly, Quarterly, and Yearly series, AMI exhibits consistent negative rank association with realised error (p ranging from -0.52 to -0.66 for higher-capacity probes), supporting its use as a triage signal. Monthly shows moderate association; Daily exhibits weaker discrimination despite measurable dependence. Across all frequencies, median forecast error decreases monotonically from low to high AMI terciles, confirming decision-relevant separation. These results establish AMI as a practical screening tool for forecasting portfolios: identifying series where sophisticated modelling is warranted, where baselines suffice, and where effort should shift from accuracy improvement to robust decision design.

翻译：预测失败并非因为模型能力不足，而是因为努力被浪费在了那些未来本质上不可知的序列上。我们提出一种建模前诊断框架，可在模型选择开始前评估特定时域的预测可行性，使实践者能将努力分配到可能产生回报的领域。我们将预测可行性操作化为滞后h处的自互信息（AMI），用以衡量过去信息对未来值不确定性的减少程度。仅使用训练数据并采用k近邻估计器，我们在涵盖六种频率的1,350条M4序列上，以季节性朴素法、ETS和N-BEATS作为探针模型，在滚动原点协议下验证了AMI与已实现样本外误差（sMAPE）的关系。核心发现是：AMI-sMAPE关系具有强烈的频率依赖性。对于周度、小时、季度和年度序列，AMI与已实现误差呈现一致的负秩相关（高容量探针的p值范围从-0.52至-0.66），支持其作为分流信号的适用性。月度序列呈现中等相关性；日度序列尽管存在可测量的依赖性，但区分能力较弱。在所有频率中，中位预测误差从低到高AMI三分位数组呈现单调递减，证实了具有决策意义的区分度。这些结果确立了AMI作为预测组合的实用筛选工具：可识别哪些序列需要复杂建模、哪些序列基线方法已足够，以及哪些序列应将努力方向从精度提升转向稳健决策设计。