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Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems

Author

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  • Raoul Nigmatullin

    (Radioelectronics and Informative-Measurement Techniques Department, Kazan National Research Technical University named after A. N. Tupolev (KNRTU-KAI), K. Marx Str., 10, 420111 Kazan, Russia)

  • Semyon Dorokhin

    (Laboratory of Multimedia Systems and Technology, Moscow Institute of Physics and Technology (MIPT), Institutskiy Per., 9, 141701 Dolgoprudny, Russia)

  • Alexander Ivchenko

    (Laboratory of Multimedia Systems and Technology, Moscow Institute of Physics and Technology (MIPT), Institutskiy Per., 9, 141701 Dolgoprudny, Russia)

Abstract

In this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider applying generalized Hurst laws to obtain a new set of reduced parameters in data associated with communication systems. We analyze three hypotheses. The first one contains one power-law exponent. The second one incorporates two power-law exponents, which are in many cases complex-conjugated. The third hypothesis has three power-law exponents, two of which are complex-conjugated as well. These hypotheses describe with acceptable accuracy (relative error does not exceed 2%) a wide set of trendless sequences (TLS) associated with radiometric measurements. Generalized Hurst laws operate with R / S curves not only in the asymptotic region, but in the entire domain. The fitting parameters can be used as the reduced parameters for the description of the given data. The paper demonstrates that this general approach can also be applied to other TLS.

Suggested Citation

  • Raoul Nigmatullin & Semyon Dorokhin & Alexander Ivchenko, 2021. "Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems," Mathematics, MDPI, vol. 9(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:381-:d:499421
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    References listed on IDEAS

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    1. Nigmatullin, R.R., 2000. "Recognition of nonextensive statistical distributions by the eigencoordinates method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(3), pages 547-565.
    2. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
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