Estimation method of Hurst exponent of fractional Brownian motion

The article contains fractional Brownian motion research, statistical estimations of Hurst exponent and their properties. This random process is used in model development, trend forecasting, in particular as special case of long-memory processes. The first recorded model with Hurst Exponent appeared in Harold Hurst’s research, published in 1951, that was dedicated to the analysis of the flow of Nil river. After that improved model of fractional Brownian motion was widely used in different financial market researches. Due to high relevance of such random processes, the problems of extrapolation of fractional Brownian motion and point estimation have become very important. This article is dedicated to the new approach of point estimation of Hurst Exponent.