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Convergence rate of CLT for the estimation of Hurst parameter of fractional Brownian motion

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  • Kim, Yoon Tae
  • Park, Hyun Suk

Abstract

In this paper, we consider the convergence of the estimator of the Hurst parameter H of a fractional Brownian motion with Hurst parameter H∈(0,1). The main goal of our work is to derive an explicit upper bound of Kolmogorov distance in order to find the information about the rate of convergence of the central limit theorems (CLT) for the estimator of the Hurst parameter.

Suggested Citation

  • Kim, Yoon Tae & Park, Hyun Suk, 2015. "Convergence rate of CLT for the estimation of Hurst parameter of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 181-188.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:181-188
    DOI: 10.1016/j.spl.2015.04.032
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    2. 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.
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