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Open AccessArticle

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

1
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
2
Laboratory of Multimedia Systems and Technology, Moscow Institute of Physics and Technology (MIPT), Institutskiy Per., 9, 141701 Dolgoprudny, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Bianca
Mathematics 2021, 9(4), 381; https://doi.org/10.3390/math9040381
Received: 22 December 2020 / Revised: 3 February 2021 / Accepted: 10 February 2021 / Published: 14 February 2021
(This article belongs to the Special Issue Fractals, Fractional Calculus and Applied Statistics)
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. View Full-Text
Keywords: hurst power-law exponent; complex systems; long-time series; power-law hypothesis hurst power-law exponent; complex systems; long-time series; power-law hypothesis
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MDPI and ACS Style

Nigmatullin, R.; Dorokhin, S.; Ivchenko, A. Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems. Mathematics 2021, 9, 381. https://doi.org/10.3390/math9040381

AMA Style

Nigmatullin R, Dorokhin S, Ivchenko A. Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems. Mathematics. 2021; 9(4):381. https://doi.org/10.3390/math9040381

Chicago/Turabian Style

Nigmatullin, Raoul; Dorokhin, Semyon; Ivchenko, Alexander. 2021. "Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems" Mathematics 9, no. 4: 381. https://doi.org/10.3390/math9040381

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