Identification of the Hurst Index of a Step Fractional Brownian Motion |
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Authors: | Albert Benassi Pierre Bertrand Serge Cohen Jacques Istas |
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Institution: | (1) Université Blaise Pascal (Clermont-Ferrand II), 63177 Aubière Cedex, France;(2) Université de Versailles St Quentin, Y. 45 Avenue des Etats Unis, 78035, Versailles;(3) Department IMSS BSHM, Université Pierre Mendes-France, F-38000 Grenoble |
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Abstract: | We propose a semi-parametric estimator for a piece-wise constant Hurst coefficient of a step fractional Brownian motion (SFBM). For the applications, we want to detect abrupt changes of the Hurst index (which represents long-range correlation) for a Gaussian process with a.s. continuous paths. The previous model of multifractional Brownian motion give a.s. discontinuous paths at change times of the Hurst index. Thus, we first propose a new kind of Fractional Brownian Motion, the SFBM and prove some (Hölder) continuity results. After, we propose an estimator of the piecewise constant Hurst parameter and prove its consistency. |
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Keywords: | change-point detection Hurst index Gaussian processes step fractional Brownian motion semi-parametric estimation |
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