Variance of permutation entropy and the influence of ordinal pattern selection

Douglas J. Little, Deb M. Kane

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Permutation entropy (PE) is a widely used measure for complexity, often used to distinguish between complex systems (or complex systems in different states). Here, the PE variance for a stationary time series is derived, and the influence of ordinal pattern selection, specifically whether the ordinal patterns are permitted to overlap or not, is examined. It was found that permitting ordinal patterns to overlap reduces the PE variance, improving the ability of this statistic to distinguish between complex system states for both numeric (fractional Gaussian noise) and experimental (semiconductor laser with optical feedback) systems. However, with overlapping ordinal patterns, the precision to which the PE variance can be estimated becomes diminished, which can manifest as increased incidences of false positive and false negative errors when applying PE to statistical inference problems.
Original languageEnglish
Article number052126
Pages (from-to)1-9
Number of pages9
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - 16 May 2017


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