A fast algorithm for robust estimates of the Hurst exponent when analyzing small samples of biometric and market data 

Vladimir I. Volchikhin, Doctor of engineering sciences, professor, president of Penza State University (40 Krasnaya street, Penza, Russia), E-mail: cnit@pnzgu.ru
Aleksandr I. Ivanov, Doctor of engineering sciences, professor, scientific adviser, Penza Scientific Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Valeriy A. Tikhomirov, Doctor of engineering sciences, professor, CEO of Scientific-production association “Razvitiye innovatsionnukh tekhnologiy” (Development of innovative technologies) (building 1, 147 Ozernaya street, Tver, Russia), E-mail: info@npo-rit.ru
Dmitriy V. Tarasov, Candidate of engineering sciences, associate professor of the sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tarasovdv@mail.ru 

Background. Currently, the Hurst exponent is quite easily interpreted in relation to biometric, medical and economic data, but it is customary to evaluate it on large samples. The purpose of the work is to reduce the sample of real data on which the Hurst exponent can be calculated quite reliably. Materials and methods. The connection between the Hurst exponent and autocorrelation functionals is used. It is proposed to reduce the problem to assessing the autocorrelation properties of the studied sequence of real data. Results and conclusions. Autocorrelation functionals relate to problems of quadratic computational complexity, while the Hurst exponent has a significantly higher computational complexity and is less stable. This makes it possible to reduce the requirements for the size of the real data sample used for calculations. 

autocorrelation functional, Hurst exponent, small samples, biometric data 

Volchikhin V.I., Ivanov A.I., Tikhomirov V.A., Tarasov D.V. A fast algorithm for robust estimates of the Hurst exponent when analyzing small samples of biometric and market data. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2024;(1):48–55. (In Russ.). doi: 10.21685/2072-3059-2024-1-4