Estimation of Hurst Parameter of Fractional Brownian Motion Using CMARS Method

TL;DR

This paper introduces a novel CMARS-based method for estimating the Hurst parameter of fractional Brownian motion, which adaptively determines spline parameters and outperforms existing techniques in simulation tests.

Contribution

The paper presents a new CMARS approach for jointly estimating the Hurst parameter and spline parameters in stochastic differential equations driven by fractional Brownian motion.

Findings

Accurately estimates Hurst parameter in simulated data

Demonstrates superiority over existing methods

Provides adaptive spline parameter estimation

Abstract

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 differentional 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 finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data. Keywords: Stochastic differential equations, fractional Brownian motion, Hurst parameter, conic multivariate adaptive regression splines