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The rate of convergence of Hurst index estimate for the stochastic differential equation

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  • Kubilius, K.
  • Mishura, Y.

Abstract

We consider a stochastic differential equation involving a pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of these estimates to the true value of a parameter is established when the diameter of interval partition tends to zero.

Suggested Citation

  • Kubilius, K. & Mishura, Y., 2012. "The rate of convergence of Hurst index estimate for the stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3718-3739.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3718-3739
    DOI: 10.1016/j.spa.2012.06.011
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    References listed on IDEAS

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    1. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
    2. Benassi, Albert & Cohen, Serge & Istas, Jacques & Jaffard, Stéphane, 1998. "Identification of filtered white noises," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 31-49, June.
    3. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    4. Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
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    Cited by:

    1. El Mehdi Haress & Alexandre Richard, 2024. "Estimation of several parameters in discretely-observed stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 641-691, October.
    2. Annie Tubadji & Vassilis Angelis & Peter Nijkamp, 2016. "Endogenous intangible resources and their place in the institutional hierarchy," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 36(1), pages 1-28, February.
    3. Yaozhong Hu & David Nualart & Hongjuan Zhou, 2019. "Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 111-142, April.
    4. Kubilius, K. & Skorniakov, V., 2016. "On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 159-167.

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