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Open AccessArticle

Relative Consistency of Sample Entropy Is Not Preserved in MIX Processes

1
Institute of Physics, University of Zielona Gora, 65-417 Zielona Gora, Poland
2
Department of Cardiology-Intensive Therapy, Poznan University of Medical Sciences Poznan, 61-701 Poznan, Poland
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(6), 694; https://doi.org/10.3390/e22060694
Received: 11 May 2020 / Revised: 14 June 2020 / Accepted: 19 June 2020 / Published: 21 June 2020
Relative consistency is a notion related to entropic parameters, most notably to Approximate Entropy and Sample Entropy. It is a central characteristic assumed for e.g., biomedical and economic time series, since it allows the comparison between different time series at a single value of the threshold parameter r. There is no formal proof for this property, yet it is generally accepted that it is true. Relative consistency in both Approximate Entropy and Sample entropy was first tested with the M I X process. In the seminal paper by Richman and Moorman, it was shown that Approximate Entropy lacked the property for cases in which Sample Entropy did not. In the present paper, we show that relative consistency is not preserved for M I X processes if enough noise is added, yet it is preserved for another process for which we define a sum of a sinusoidal and a stochastic element, no matter how much noise is present. The analysis presented in this paper is only possible because of the existence of the very fast NCM algorithm for calculating correlation sums and thus also Sample Entropy. View Full-Text
Keywords: time series analysis; sample entropy; relative consistency time series analysis; sample entropy; relative consistency
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Żurek, S.; Grabowski, W.; Wojtiuk, K.; Szewczak, D.; Guzik, P.; Piskorski, J. Relative Consistency of Sample Entropy Is Not Preserved in MIX Processes. Entropy 2020, 22, 694.

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