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Asymptotic Normality of the Estimators for Fractional Brownian Motions with Discrete Data

Author

Listed:
  • Lin Sun
  • Xiaojian Yu
  • Xuewei Guan
  • Qinghao Meng

Abstract

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.

Suggested Citation

  • Lin Sun & Xiaojian Yu & Xuewei Guan & Qinghao Meng, 2014. "Asymptotic Normality of the Estimators for Fractional Brownian Motions with Discrete Data," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:323091
    DOI: 10.1155/2014/323091
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    References listed on IDEAS

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    2. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    3. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    4. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
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