Conditional entropy of ordinal patterns

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern. We observe that this quantity provides a good estimation of the Kolmogorov Sinai entropy in many cases. In particular, the conditional entropy of ordinal patterns of a finite order coincides with the Kolmogorov Sinai entropy for periodic dynamics and for Markov shifts over a binary alphabet. Finally, the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real-world data. (C) 2013 Elsevier B.V. All rights reserved.