Estimation of the Hurst Parameter for Fractional Brownian Motion Using the Cmars Method

Abstract

In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data.