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Multi-scale entropy analysis and Hurst exponent

Author

Listed:
  • Mollaei, Saeid
  • Darooneh, Amir Hossein
  • Karimi, Somaye

Abstract

Several methods exist for measuring the complexity in a system through analysis of its associated time series. Multi-scale entropy appears as a successful method on this matter. It has been applied in many disciplines with great achievements. For example by analysis of the bio-signals, we are able to diagnose various diseases. However, in most versions for the multi-scale entropy the examined time series is analyzed qualitatively. In this study, we try to present a quantitative picture for the multi-scale entropy analysis. Particularly, we focus on finding relation between the result of the multi-scale analysis and the Hurst exponent which quantifies the persistence in time series. For this purpose, the fractional Gaussian noise time series with different Hurst exponents are analyzed by the multi-scale entropy method and the results are fitted to a decreasing q-exponential function. We observe remarkable relation between the function parameters and Hurst exponent. This function can simulate the result of analysis for the white noise to the 1∕f noise.

Suggested Citation

  • Mollaei, Saeid & Darooneh, Amir Hossein & Karimi, Somaye, 2019. "Multi-scale entropy analysis and Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    • Handle: RePEc:eee:phsmap:v:528:y:2019:i:c:s0378437119307812
    DOI: 10.1016/j.physa.2019.121292
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    Cited by:

    1. Zeinali, Narges & Pourdarvish, Ahmad, 2022. "An entropy-based estimator of the Hurst exponent in fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    2. Jia, Linlu & Ke, Jinchuan & Wang, Jun, 2020. "Fluctuation behavior analysis of stochastic exclusion financial dynamics with random jump," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).

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