Time Series Forecastability Measures

2025-07-17

AI Summary

This paper addresses the lack of a quantitative predictability metric prior to time-series modeling. We propose a model-free pre-assessment framework that jointly quantifies intrinsic predictability via two complementary indicators: the spectral regularity score (capturing frequency-domain structure) and the maximum Lyapunov exponent (measuring chaotic dynamics). To our knowledge, this is the first work integrating linear spectral analysis with nonlinear dynamical systems theory for predictability assessment—shifting from conventional post-hoc, model-dependent evaluation to a theory-driven, priori feasibility criterion. Empirical validation on synthetic benchmarks and the real-world M5 retail sales dataset demonstrates statistically significant negative correlations (p < 0.01) between both metrics and prediction errors of diverse models—including ARIMA, LSTM, and N-BEATS—confirming their effectiveness in identifying highly predictable series and enabling principled allocation of forecasting resources.

Technology Category

• Machine Learning: Evaluation and Analysis
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

This paper proposes using two metrics to quantify the forecastability of time series prior to model development: the spectral predictability score and the largest Lyapunov exponent. Unlike traditional model evaluation metrics, these measures assess the inherent forecastability characteristics of the data before any forecast attempts. The spectral predictability score evaluates the strength and regularity of frequency components in the time series, whereas the Lyapunov exponents quantify the chaos and stability of the system generating the data. We evaluated the effectiveness of these metrics on both synthetic and real-world time series from the M5 forecast competition dataset. Our results demonstrate that these two metrics can correctly reflect the inherent forecastability of a time series and have a strong correlation with the actual forecast performance of various models. By understanding the inherent forecastability of time series before model training, practitioners can focus their planning efforts on products and supply chain levels that are more forecastable, while setting appropriate expectations or seeking alternative strategies for products with limited forecastability.

Problem

• Quantify time series forecastability before model development
• Assess inherent forecastability using spectral and chaos metrics
• Evaluate forecastability correlation with actual model performance

Innovation

• Spectral score measures frequency regularity
• Lyapunov exponent quantifies system chaos
• Pre-model forecastability assessment metrics