Estimation of Hurst Parameter of Fractional Brownian Motion Using CMARS Method

Fatma Yerlikaya Ozkurt, Ceren Vardar Acar, Yeliz Yolcu Okur, Gerhard Wilhelm Weber

Published 2013-02-14Version 1

In this study, we develop a new theory of estimating Hurst parame- ter using conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solution of stochastic di?erentional equations (SDEs) driven by fractional Brownian motion (fBm). The superiority of our approach to the others is, it not only estimates the Hurst parameter but also ?nds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data. Keywords: Stochastic di?erential equations, fractional Brownian motion, Hurst parameter, conic multivariate adaptive regression splines