Recurrence plots analysis

Krzysztof Urbanowicz
Faculty of Physics, Warsaw University of Technology
ul. Koszykowa 75, 00-662 Warszawa
e-mail: urbanow@if.pw.edu.pl

The quantitative features of recurrence plots [1] are analyzed. The way to estimate optimal method parameters, such as embedding dimension and delay, is introduced. In comparison to the publication [2], where the correlation entropy K2, was extracted using the maximum norm, it was found that the Euclidean norm allows to find the Kolmogorov entropy K1. Another formula was found that shows the connection between the average line length in recurrence plot and the Kolmogorov entropy. The method to estimate amount of noise in time series with a help of recurrence plot was developed. Several time series with known additive and dynamical noise were analyzed using this method, giving good results. The estimation of noise-to-signal ratio for real economical data was performed.

[1] J-P.Eckmann, S.Kamphorst, D.Ruelle, "Recurrence plots of dynamical systems", Europhys. Lett. 4, 973-977 (1987).
[2] P.Faure, H.Korn, "A new method to estimate the Kolmogorov entropy
from recurrence plots: it's application to neuronal signals", Physica D 122,265-279 (1998).
[3] K. Pawelzik and H. G. Schuster, "Generalized dimensions and entropies from a measured time series", Phys. Rev. 35 A, 481 (1987).
[4] Fatihcan M. Atay, Yigit Altintas, "Recovering smooth dynamics from time series with the aid of recurrence plots", Phys. Rev. E 59(6), 6593(6) (1999).