Estimating a generating partition from observed time series: symbolic shadowing.
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.
Centre for Applied Dynamics and Optimization, School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. yoshito@maths.uwa.edu.au
Yoshito
Y
Hirata
Kevin
K
Judd
Devin
D
Kilminster