Small Order Patterns in Big Time Series: A Practical Guide
Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany
Received: 30 April 2019 / Revised: 29 May 2019 / Accepted: 18 June 2019 / Published: 21 June 2019
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The study of order patterns of three equally-spaced values
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.
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Bandt, C. Small Order Patterns in Big Time Series: A Practical Guide. Entropy 2019, 21, 613.
Bandt C. Small Order Patterns in Big Time Series: A Practical Guide. Entropy. 2019; 21(6):613.
Bandt, Christoph. 2019. "Small Order Patterns in Big Time Series: A Practical Guide." Entropy 21, no. 6: 613.
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