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Comparison of the LS-based estimators and the MLE for the fractional Ornstein–Uhlenbeck process

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  • Katsuto Tanaka

    (Gakushuin University)

Abstract

We deal with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm), where the drift parameter $$\alpha $$ α of the fO–U process is any unknown real number, whereas the Hurst index H of the fBm belongs to (0, 1) and is assumed to be known. Under this setting we consider the least squares (LS)-based estimators and the maximum likelihood estimator (MLE) of $$\alpha $$ α , and examine the efficiencies of the LS-based estimators relative to the MLE, paying attention to the effect of the sign of $$\alpha $$ α and the value of H. It is found that the MLE is more efficient than the LSE when $$\alpha \ne 0$$ α ≠ 0 , but the LSE is more efficient when $$\alpha =0$$ α = 0 .

Suggested Citation

  • Katsuto Tanaka, 2020. "Comparison of the LS-based estimators and the MLE for the fractional Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 415-434, July.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:2:d:10.1007_s11203-020-09215-3
    DOI: 10.1007/s11203-020-09215-3
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    References listed on IDEAS

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    1. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    2. 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.
    3. Alexandre Brouste & Marina Kleptsyna, 2010. "Asymptotic properties of MLE for partially observed fractional diffusion system," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 1-13, April.
    4. Tanaka, Katsuto, 2014. "Distributions Of Quadratic Functionals Of The Fractional Brownian Motion Based On A Martingale Approximation," Econometric Theory, Cambridge University Press, vol. 30(5), pages 1078-1109, October.
    5. Katsuto Tanaka, 2015. "Maximum likelihood estimation for the non-ergodic fractional Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 315-332, October.
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