What is it about?

Time series - sequences of values - are key data in financial markets, heart and brain signals, weather, environtmental and earthquake monitoring etc. Huge amounts of data must be processed automatically which requires simple, fast, and robust methods. For this purpose, it is appropriate to study order patterns of successive values rather than the values themselves. The permutation entropy introduced by the author and Bernd Pompe in 2001 has found a lot of applications in most different fields. Here we discuss still simpler parameters. One example is the turning rate - the relative number of maxima and minima in a noisy time series.

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Why is it important?

As an example, consider an EEG (electroencephalographic) brain measurement during one night of sleep. With 500 values per second, a single channel provides 15 millions of values. Experts or automated systems carefully analyse several channels and combine with an eye-tracker to classify sleep stages for every 30 seconds. If we determine the turning rate for every 30 seconds, we get a short time series of only 1000 values which directly show the sleep depth without using sophisticated rules. Similar applications for EEG data include the study of epilepsy and Alzheimer's disease, the effects of drugs, and the control of anesthesia. Order patterns apply to all other fields where time series occur.


With an ever-increasing amount of time series data, such methods become more important. On the mathematical side, this requires the investigation of longer order patterns and the construction of models of random order.

Christoph Bandt
Ernst-Moritz-Arndt Universitat Greifswald

Read the Original

This page is a summary of: Statistics and contrasts of order patterns in univariate time series, Chaos An Interdisciplinary Journal of Nonlinear Science, March 2023, American Institute of Physics,
DOI: 10.1063/5.0132602.
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