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An Exponential Nonuniform Berry–Esseen Bound for the Fractional Ornstein–Uhlenbeck Process

Author

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  • Hui Jiang

    (Nanjing University of Aeronautics and Astronautics)

  • Jingying Zhou

    (Nanjing University of Aeronautics and Astronautics)

Abstract

In this paper, we study the asymptotic properties of the maximum likelihood estimator of the drift parameter in the fractional Ornstein–Uhlenbeck process. Using the change of measure method and asymptotic analysis technique, we establish an exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator. As an application, the optimal uniform Berry–Esseen bound and Cramér-type moderate deviation are obtained.

Suggested Citation

  • Hui Jiang & Jingying Zhou, 2023. "An Exponential Nonuniform Berry–Esseen Bound for the Fractional Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1037-1058, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01194-w
    DOI: 10.1007/s10959-022-01194-w
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    References listed on IDEAS

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    1. Es-Sebaiy, Khalifa & Viens, Frederi G., 2019. "Optimal rates for parameter estimation of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3018-3054.
    2. Qingpei Zang & Lixin Zhang, 2019. "Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes," Journal of Theoretical Probability, Springer, vol. 32(1), pages 183-201, March.
    3. 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.
    4. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    5. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic Theory For Estimating Drift Parameters In The Fractional Vasicek Model," Econometric Theory, Cambridge University Press, vol. 35(1), pages 198-231, February.
    6. 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.
    7. 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.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. M.L. Kleptsyna & A. Le Breton & M.-C. Roubaud, 2000. "Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 173-182, January.
    11. 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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