Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths

  • Jean-François Coeurjolly

DOI: 10.1023/A:1017507306245

Cite this article as:
Coeurjolly, JF. Statistical Inference for Stochastic Processes (2001) 4: 199. doi:10.1023/A:1017507306245


This paper develops a class of consistent estimators of the parameters of a fractional Brownian motion based on the asymptotic behavior of the k-th absolute moment of discrete variations of its sampled paths over a discrete grid of the interval [0,1]. We derive explicit convergence rates for these types of estimators, valid through the whole range 0 < H < 1 of the self-similarity parameter. We also establish the asymptotic normality of our estimators. The effectiveness of our procedure is investigated in a simulation study.

fractional Brownian motion fractional Gaussian noise discrete variations consistency self-similarity 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Jean-François Coeurjolly
    • 1
  1. 1.IMAG-LMCUniversity Joseph FourierGrenoble Cedex 09France

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