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Open AccessArticle

Small Order Patterns in Big Time Series: A Practical Guide

Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany
Entropy 2019, 21(6), 613; https://doi.org/10.3390/e21060613
Received: 30 April 2019 / Revised: 29 May 2019 / Accepted: 18 June 2019 / Published: 21 June 2019
The study of order patterns of three equally-spaced values x t , x t + d , x t + 2 d in a time series is a powerful tool. The lag d is changed in a wide range so that the differences of the frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, and outliers and missing data do not matter. On the theoretical side, we study the properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions. View Full-Text
Keywords: permutation entropy; autocorrelation; time series; order pattern; signal processing permutation entropy; autocorrelation; time series; order pattern; signal processing
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Bandt, C. Small Order Patterns in Big Time Series: A Practical Guide. Entropy 2019, 21, 613.

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