On the features of Hurst Exponent estimates of the Fractional Brownian motion calculated by the R/S-analysis

Abstract The article presents the analysis results of the dependence of the accuracy in estimating Hurst exponent of the Fractional Brownian motion by the R/S-analysis towards the method parameters Lmin , Lmax . It is found that the estimation of the Hurst exponent coinciding with its corresponding value is used to generate Fractional Brownian H〈mod〉 motion only when <?CDATA ${L}_{\max }\,=\,{L}_{\max }^{\langle true\rangle }$?> L max = L max 〈 t r u e 〉 . Otherwise, Hurst Exponent Estimate H depending on the value Lmax varies in the span [0.25; 1.12]. The result obtained points out that it is necessary to critically revise the results of a number of studies where in order to analyze and forecast the dynamics of complex systems of different nature (for example, in economic ones) the authors employed the R/S-evaluation exponents of the Hurst exponent H of the time series (TS), composed of the exponents characterizing the state of the given system at a certain point.