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

Mathematics. 2021. Vol. 9. No. 4. Article 381.

Nigmatullin R. R., Dorokhin S. V., Ivchenko A.

n 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.

Keywords: показатель Херста, анализ временных рядов, analysis of time series, SDR, Software defined radio, hurst power-law exponent