Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems
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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
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Revised: 3 February 2021
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Accepted: 10 February 2021
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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
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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 StyleNigmatullin, Raoul, Semyon Dorokhin, and Alexander Ivchenko. 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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