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arXiv · 2601.10006

Horizon-resolved Forecastability of Time Series via Auto Mutual Information

Peter Maurice Catt
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Abstract

In many social, business, economic, and physical systems the true data-generating process is rarely known, so a series forecastability cannot be assumed; it must be assessed from the observed history. This paper evaluates a horizon-specific, pre-modelling measure for that assessment: auto-mutual information (AMI), a training-only measure of past-future dependence at each forecast horizon; higher AMI indicates more recoverable temporal structure. It is evaluated on the M4 Monthly dataset (47,992 of 48,000 series, 18-month horizon) with seasonal naive, ETS, and N-BEATS as probes and MASE as the error measure. The series-level association with realised skill is modest but systematic (mean Spearman p of 0.11 to 0.13 for ETS and N-BEATS), accumulating into a pronounced descriptive gradient: median MASE is 29% (ETS) to 37% (N-BEATS) lower in the top within-horizon AMI decile than in the bottom. AMI outperforms absolute autocorrelation as a horizon-specific diagnostic by a small, consistent margin; paired bootstrap intervals exclude zero for all three probes, and synthetic benchmarks with analytically exact AMI locate the advantage on nonlinear dependence. Decile assignments are sample-relative and require recalibration on a new portfolio. The contribution is a pre-modelling diagnostic, not a forecasting model.

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Peter Maurice Catt. 2026-01-15. Horizon-resolved Forecastability of Time Series via Auto Mutual Information. https://arxiv.org/abs/2601.10006

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