Model-free quantification of time-series predictability

Joshua Garland, Ryan James, and Elizabeth Bradley
Phys. Rev. E 90, 052910 – Published 12 November 2014

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 nonstationarity of the generating process, as well as from measurement issues such as 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.

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  • Received 27 April 2014
  • Revised 5 August 2014

DOI:https://doi.org/10.1103/PhysRevE.90.052910

©2014 American Physical Society

Authors & Affiliations

Joshua Garland1,*, Ryan James1,†, and Elizabeth Bradley1,2,‡

  • 1Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado 80309, USA
  • 2Santa Fe Institute, Santa Fe, New Mexico 87501, USA

  • *joshua.garland@colorado.edu
  • ryan.james@colorado.edu
  • lizb@colorado.edu

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Issue

Vol. 90, Iss. 5 — November 2014

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