Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:B2L-C
Session:
Number:B2L-C4
Log-Log-Step Method for Detection of Patterns Within Randomness Quantitatively Assessed
Florian Gomez, Ruedi Stoop,
pp.419-422
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
It has been demonstrated earlier by us that staircase-like structures in the log-log correlation plot of a time series provide an indicator of underlying patterns, even in conditions of strong noisy or/and jittered data. In this article, we analyze the method under different jitternoise-configurations and define quantitative measures for the method’s applicability. A phase diagram shows the remarkable potential of this method even under very unfavorable conditions of noise and jitter. Moreover, we provide a novel and much more compact analytical derivation of the upper and lower bounds on the number of steps observable in the ideal noiseless case, as a function of pattern length and embedding dimension.