Kullback-Leibler Approach to Chaotic Time Series

Abstract

We focus discussion on extracting probability distribution functions (PDFs) from semi-chaotic time series (TS). We wish to ascertain what is the best extraction approach and to such an end we use an extremely well known semiclassical system in its classical limit [1, 2]. Since this systems possesses a very rich dynamics, it can safely be regarded as representative of many other physical scenarios. In discussing this ?extraction? problem, we consider the two most natural approaches, namely, i) histograms and ii) the Bandt?Pompe technique. We use the Kullback-Leibler relative entropy to compare the information content of the concomitant PDFs.