Model-free quantification of time-series predictability

TL;DR

This paper introduces a model-free heuristic based on weighted permutation entropy to assess the predictability of complex time series, helping practitioners identify when forecast methods are unsuitable due to the data's inherent complexity.

Contribution

It proposes a novel, model-free approach using weighted permutation entropy to quantify time series complexity and predictability, validated across 120 datasets.

Findings

Redundancy correlates with predictability in time series.

Weighted permutation entropy effectively estimates data complexity.

The heuristic guides practitioners in selecting appropriate forecasting methods.

Abstract

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data---which results from the dimension, nonlinearity, and non-stationarity of the generating process, as well as from measurement issues like noise, aggregation, and finite data length---is both empirically quantifiable and directly correlated with predictability. In particular, we argue that redundancy is an effective way to measure complexity and predictive structure in an experimental time series and that weighted permutation entropy is an effective way to estimate that redundancy. To validate these conjectures, we study 120 different time-series data sets. For each time series, we construct predictions using a wide variety of forecast models, then compare the accuracy of the predictions with the permutation entropy of that time series. We use the results to develop a model-free heuristic that can help practitioners recognize when a particular prediction method is not well matched to the task at hand: that is, when the time series has more predictive structure than that method can capture and exploit.