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Maximum likelihood estimation for the non-ergodic fractional Ornstein–Uhlenbeck process

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  • Katsuto Tanaka

Abstract

For the non-ergodic fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion, we deal with the maximum likelihood estimator (MLE) 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 distribution of the MLE, and explore its distributional properties by paying attention to the influence of $$H$$ H and the sampling span $$T$$ T . We also derive the asymptotic distribution of the MLE as $$T$$ T becomes large. It is shown that, unlike the ergodic case, the asymptotic distribution depends on $$H$$ H . We further consider the unit root testing problem in the fO–U process and compute the powers of the test based on the MLE. Copyright Springer Science+Business Media Dordrecht 2015

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  • 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.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:3:p:315-332
    DOI: 10.1007/s11203-014-9110-9
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    References listed on IDEAS

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    1. Bercu, Bernard & Coutin, Laure & Savy, Nicolas, 2012. "Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3393-3424.
    2. 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.
    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. 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. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.
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    4. 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.

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