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Small Order Patterns in Big Time Series: A Practical Guide
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: Received: 30 April 2019 / Approved: 5 May 2019 / Online: 5 May 2019 (12:50:33 CEST)
A peer-reviewed article of this Preprint also exists.
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, 613.
Abstract
The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of 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, outliers and missing data do not matter. On the theoretical side, we study 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.
Keywords
permutation entropy; autocorrelation; time series; order pattern
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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