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Drift parameter estimation in fractional diffusions driven by perturbed random walks

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  • Bertin, Karine
  • Torres, Soledad
  • Tudor, Ciprian A.

Abstract

We estimate the drift parameter in a simple linear model driven by fractional Brownian motion. We propose maximum likelihood estimators (MLE) for the drift parameter construct by using a random walk approximation of the fractional Brownian motion.

Suggested Citation

  • Bertin, Karine & Torres, Soledad & Tudor, Ciprian A., 2011. "Drift parameter estimation in fractional diffusions driven by perturbed random walks," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 243-249, February.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:243-249
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    References listed on IDEAS

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    1. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    2. Tommi Sottinen & Ciprian Tudor, 2008. "Parameter estimation for stochastic equations with additive fractional Brownian sheet," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 221-236, October.
    3. M.L. Kleptsyna & A. Le Breton, 2002. "Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 229-248, October.
    4. Le Breton, Alain, 1998. "Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 263-274, June.
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    Cited by:

    1. Cai, Chunhao & Cheng, Xuwen & Xiao, Weilin & Wu, Xiang, 2019. "Parameter identification for mixed fractional Brownian motions with the drift parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    2. Nenghui Kuang & Huantian Xie, 2015. "Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 75-91, February.
    3. Alexandre Brouste & Stefano Iacus, 2013. "Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package," Computational Statistics, Springer, vol. 28(4), pages 1529-1547, August.

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