The Knowable Future: Mapping the Decay of Past–Future Mutual Information Across Forecast Horizons

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 Naïve, 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 ρ 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.