Estimating a generating partition from observed time series: Symbolic shadowing

Yoshito Hirata, Kevin Judd, and Devin Kilminster
Phys. Rev. E 70, 016215 – Published 30 July 2004

Abstract

We propose a deterministic algorithm for approximating a generating partition from a time series using tessellations. Using data generated by Hénon and Ikeda maps, we demonstrate that the proposed method produces partitions that uniquely encode all the periodic points up to some order, and provide good estimates of the metric and topological entropies. The algorithm gives useful results even with a short noisy time series.

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  • Received 18 July 2003

DOI:https://doi.org/10.1103/PhysRevE.70.016215

©2004 American Physical Society

Authors & Affiliations

Yoshito Hirata*, Kevin Judd, and Devin Kilminster

  • Centre for Applied Dynamics and Optimization, School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia

  • *Electronic address: yoshito@maths.uwa.edu.au
  • Electronic address: kevin@maths.uwa.edu.au
  • Electronic address: devin@maths.uwa.edu.au

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Issue

Vol. 70, Iss. 1 — July 2004

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