Method for Estimating the Hurst Exponent of Fractional Brownian Motion

Abstract—Fractional Brownian motion is studied. Statistical estimators of the Hurst exponent are proposed, and their properties are examined. This stochastic process is widely used in model development, trend forecasting, and, in particular, as a special case of long-memory processes. The first model involving the Hurst exponent appeared in the British hydrologist Harold Hurst’s research published in 1951, where he analyzed the flow of the Nile River. Later, an improved model of fractional Brownian motion was widely used in different financial market studies. Since such stochastic processes are of great interest, the extrapolation of fractional Brownian motion and the point estimation of the Hurst exponent H have become important problems. A new approach to the point estimation of the Hurst exponent is proposed in this article.