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Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method. (English) Zbl 1314.62079

Summary: 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.

MSC:

62F10 Point estimation
60G22 Fractional processes, including fractional Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Software:

CMARS
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Full Text: DOI arXiv

References:

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