In many social, business, economic, and physical systems, the true data generating process (DGP) is unknown and forecasters must therefore work with the observed time series. We propose a pre-modelling diagnostic framework that assesses horizon-specific forecastability before model selection begins, helping decide when additional modelling effort is likely to pay off. We operationalise forecastability as auto-mutual information (AMI) at lag h, measuring how much the past reduces uncertainty about future values. Using a k-nearest-neighbour estimator computed on training data only, we validate AMI against realised out-of-sample error (sMAPE) across 1,350 M4 series spanning six frequencies, using 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 Hourly, Weekly, Quarterly, and Yearly series, AMI shows consistent negative rank association with realised error (Spearman rho from -0.52 to -0.66 for higher-capacity probes), supporting its use as a triage signal; Monthly shows moderate association, while 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 identifying when sophisticated modelling is warranted, when simple baselines are likely to suffice, and when attention should shift from accuracy improvement to robust decision design. These results support the use of horizon-specific forecastability diagnostics to guide modelling effort and resource allocation in organisational forecasting settings.

翻译：在许多社会、商业、经济和物理系统中，真实的数据生成过程（DGP）是未知的，因此预测者必须基于观测到的时间序列开展工作。我们提出一种建模前诊断框架，在模型选择开始前评估特定预测视界的可预测性，以帮助判断何时投入额外的建模努力可能产生回报。我们将可预测性操作化为滞后h处的自互信息（AMI），用以衡量过去信息能在多大程度上减少未来值的不确定性。通过仅使用训练数据计算的k近邻估计器，我们在涵盖六种频率的1,350条M4序列上，以滚动原点评估方案下的季节性朴素法、ETS和N-BEATS作为探测模型，验证了AMI与已实现样本外误差（sMAPE）的关系。核心发现表明：AMI-sMAPE关系具有强烈的频率依赖性。对于小时、周、季度和年度序列，AMI与已实现误差呈现一致的负秩相关（高容量探测模型的斯皮尔曼相关系数ρ介于-0.52至-0.66），支持其作为预测能力分级信号；月度序列呈现中等相关性，而日度序列虽存在可测的依赖性但区分能力较弱。在所有频率中，预测误差中位数从低AMI三分位组到高AMI三分位组呈现单调递减，证实了具有决策意义的区分度。这些结果确立了AMI作为一种实用筛选工具的价值，可用于识别何时需要复杂建模、何时简单基线方法可能足够、以及何时应将关注点从精度提升转向稳健决策设计。本研究支持在组织预测场景中使用特定预测视界的可预测性诊断来指导建模努力和资源分配。