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Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process

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  • Katsuto Tanaka

Abstract

We discuss some inference problems associated with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter $$H$$ H is known and is in $$[1/2, 1)$$ [ 1 / 2 , 1 ) . Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) for the drift parameter, and explore their distributional properties by paying attention to the influence of $$H$$ H and the sampling span $$M$$ M . We also deal with the ordinary least squares estimator (OLSE) and examine the asymptotic relative efficiency. It is shown that the MCE is asymptotically efficient, while the OLSE is inefficient. We also consider the unit root testing problem in the fO–U process and compute the power of the tests based on the MLE and MCE. Copyright Springer Science+Business Media Dordrecht 2013

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  • Katsuto Tanaka, 2013. "Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 173-192, October.
    • Handle: RePEc:spr:sistpr:v:16:y:2013:i:3:p:173-192
    DOI: 10.1007/s11203-013-9085-y
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    References listed on IDEAS

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    1. 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.
    2. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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    Cited by:

    1. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    2. Li, Jia & Phillips, Peter C. B. & Shi, Shuping & Yu, Jun, 2022. "Weak Identification of Long Memory with Implications for Inference," Economics and Statistics Working Papers 8-2022, Singapore Management University, School of Economics.
    3. Katsuto Tanaka & Weilin Xiao & Jun Yu, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    4. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    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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