arXiv subjects

Peter Maurice Catt

Publications and source records attributed to Peter Maurice Catt.

3 recordsLinked to original sources

arXiv2026

Horizon-resolved Forecastability of Time Series via Auto Mutual Information

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.

stat.AP↗

arXiv2026

On the Limits of Prediction: Forecastability Profiles and Information Decay in Time Series

Forecasting accuracy is bounded by the information available about the future. This paper makes that statement precise using information-theoretic tools. Under logarithmic loss, the expected performance of any probabilistic forecast decomposes into two parts: an irreducible component and an approximation component. The irreducible term is the conditional entropy of the future given the available information, while the approximation term is the divergence between the true conditional distribution and the forecasting method. The gap between this conditional-entropy limit and an unconditional baseline is exactly the mutual information between the future observation and the declared information set. This leads to a definition of forecastability as the maximum achievable reduction in expected log loss. Evaluated across horizons, forecastability forms a profile that describes how predictive information varies with lead time. This profile reflects the dependence structure of the process and need not be monotone: predictive information may be concentrated at particular lags, including seasonal horizons, even when intermediate horizons contain little useful signal. From this profile, the paper defines the informative horizon set: the horizons at which forecastability exceeds a practical threshold. At horizons not in this set, the achievable gain over the unconditional baseline is necessarily small, regardless of the forecasting method used. The framework therefore separates what is learnable from what is not, and distinguishes limits imposed by the data from errors introduced by modelling. The result is a pre-modelling diagnostic that identifies where meaningful prediction is feasible before any model is chosen, providing a principled basis for allocating modelling effort across forecast horizons.

stat.AP↗

arXiv2026

Forecastability as an Information-Theoretic Limit on Prediction

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.

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