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Permutation entropy and order patterns in long time series. (English) Zbl 1366.62088

Rojas, Ignacio (ed.) et al., Time series analysis and forecasting. Selected contributions from the international work-conference on time series, ITISE conference, Granada, Spain, July 2015. Cham: Springer (ISBN 978-3-319-28723-2/hbk; 978-3-319-28725-6/ebook). Contributions to Statistics, 61-73 (2016).
Summary: While ordinal techniques are commonplace in statistics, they have been introduced to time series fairly recently by M. Hallin and M. L. Puri [J. Multivariate Anal. 50, No. 2, 175–237 (1994; Zbl 0805.62050)]. Permutation entropy, an average of frequencies of order patterns, was suggested by C. Bandt et al. [Nonlinearity 15, No. 5, 1595–1602 (2002; Zbl 1026.37027)] and used by many authors as a complexity measure in physics, medicine, engineering, and economy. Here a modified version is introduced, the “distance to white noise”.
For datasets with tens of thousands or even millions of values, which are becoming standard in many fields, it is possible to study order patterns separately, determine certain differences of their frequencies, and define corresponding autocorrelation type functions. In contrast to classical autocorrelation, these functions are invariant with respect to nonlinear monotonic transformations of the data. For order three patterns, a variance-analytic “Pythagoras formula” combines the different autocorrelation functions with our new version of permutation entropy. We demonstrate the use of such correlation type functions in sliding window analysis of biomedical and environmental data.
For the entire collection see [Zbl 1352.62009].

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
94A17 Measures of information, entropy
62P10 Applications of statistics to biology and medical sciences; meta analysis

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References:

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