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Estimating the Hurst Parameter

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Abstract

Let \(\{b_{H}(t),\, t\in \mathbb{R}\}\) be a fractional Brownian motion with parameter 0 <  H  <  1. We are interested in the estimation of this parameter. To achieve this goal, we consider certain functionals of the second order increments of b H (·), using variation technics. Based on an almost-sure convergence theorem for general functionals, we single out particular functionals that allows to construct certain regression models for the parameter H. We show that this regression based estimator for H is asymptotically unbiased, consistent and that it satisfies a Central Limit Theorem.

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Authors and Affiliations

  1. LabSAD, BSHM, Université Pierre Mendès-France, 1251 Avenue centrale, BP 47, 38040, Grenoble cedex 9, France

    Corinne Berzin

  2. Escuela de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, Paseo Los Ilustres, Los Chaguaramos, A.P., 47197, Caracas, 1041-A, Venezuela

    José León

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  1. Corinne Berzin
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  2. José León
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Correspondence to Corinne Berzin.

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Berzin, C., León, J. Estimating the Hurst Parameter. Stat Infer Stoch Process 10, 49–73 (2007). https://doi.org/10.1007/s11203-005-0059-6

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  • DOI: https://doi.org/10.1007/s11203-005-0059-6

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