An Information-Theoretic Diagnostic Analytics Framework for Mapping Past-Future Dependence in Horizon-Specific Forecastability
Peter Maurice Catt

TL;DR
This paper introduces a diagnostic framework using auto-mutual information to assess horizon-specific forecastability of time series, aiding in model selection and resource allocation before modeling begins.
Contribution
It proposes a novel, information-theoretic diagnostic method for evaluating forecastability that is validated across diverse real-world time series datasets.
Findings
Auto-mutual information negatively correlates with forecast error in most frequencies.
Median forecast error decreases from low to high forecastability terciles.
The framework effectively distinguishes series where advanced models add value from those suitable for simple baselines.
Abstract
In many systems, the true data-generating process is unknown, requiring forecasters to rely on observed time series. This study proposes a pre-modeling diagnostic framework for horizon-specific forecastability assessment that evaluates forecastability before model selection begins. Forecastability is operationalized using auto-mutual information at lag h, which quantifies how much past observations reduce uncertainty about future values, estimated via a k-nearest-neighbor estimator computed strictly on training data to preserve out-of-sample validity. The diagnostic signal is validated against realized out-of-sample symmetric mean absolute percentage error across 42,355 time series spanning six temporal frequencies, using benchmark and higher-capacity probe models under a rolling-origin protocol. The results reveal a strong frequency-dependent relationship between measurable dependence…
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Taxonomy
TopicsForecasting Techniques and Applications · Stock Market Forecasting Methods · Ecosystem dynamics and resilience
