HURST EXPONENT ESTIMATES ON SMALL SAMPLES: THE SIMPLEST VERSION OF FEDER'S NON-LINEAR METHOD ERROR COMPENSATOR FOR MODELING ECONOMIC AND BIOMETRIC DATA 

Aleksandr I. Ivanov, Doctor of technical sciences, associate professor, scientific consultant, Penza Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Dmitriy V. Tarasov, Candidate of technical 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
Kirill A. Gorbunov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: kirill.gorbunov@gmail.com 

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 aim of the work is to eliminate the methodological error that occurs due to small samples of real data. Materials and methods. The simulation of two-dimensional Brownian motion is used, which gives rise to the possibility of calculating the Hurst exponents. It is proposed by means of simulation modeling to build in advance a nonlinear corrector of methodological errors discovered earlier by E. Feder. Results and conclusions. A relation has been obtained for the value of methodological errors in estimating the Hurst exponent, which makes it possible to correct estimates for small values of the exponent H<0.35 and large values of the exponent H > 0.65. The need to correct methodological errors is growing as the size of small samples of real economic and biometric data decreases. 

autocorrelation functional, Hurst exponent, small samples, biometric data, methodological error, error corrector 

Ivanov A.I., Tarasov D.V., Gorbunov K.A. Hurst exponent estimates on small samples: the simplest version of Feder's non-linear method error compensator for modeling economic and biometric data. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2023;(3):50–54. (In Russ.). doi: 10.21685/2307-4205-2023-3-6