Asymptotic normality of the estimators for fractional Brownian motions with discrete data. (English) Zbl 1473.62298

Summary: This paper deals with the problem of estimating the Hurst parameter in the fractional Brownian motion when the Hurst index is greater than one half. The estimation procedure is built upon the marriage of the autocorrelation approach and the maximum likelihood approach. The asymptotic properties of the estimators are presented. Using the Monte Carlo experiments, we compare the performance of our method to existing ones, namely, R/S method, variations estimators, and wavelet method. These comparative results demonstrate that the proposed approach is effective and efficient.


62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
60G22 Fractional processes, including fractional Brownian motion
93E10 Estimation and detection in stochastic control theory


Hurst parameter


Full Text: DOI


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