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Parameter estimation for reflected Ornstein–Uhlenbeck processes with discrete observations

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Listed:
  • Yaozhong Hu
  • Chihoon Lee
  • Myung Lee
  • Jian Song

Abstract

A parameter estimation problem for a one-dimensional reflected Ornstein–Uhlenbeck is considered. We assume that only the state process itself (not the local time process) is observable and the observations are made only at discrete time instants. Strong consistency and asymptotic normality are established. Our approach is of the method of moments type and is based on the explicit form of the invariant density of the process. The method is valid irrespective of the length of the time intervals between consecutive observations. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Yaozhong Hu & Chihoon Lee & Myung Lee & Jian Song, 2015. "Parameter estimation for reflected Ornstein–Uhlenbeck processes with discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 279-291, October.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:3:p:279-291
    DOI: 10.1007/s11203-014-9112-7
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    References listed on IDEAS

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    1. Lijun Bo & Yongjin Wang & Xuewei Yang, 2010. "Some integral functionals of reflected SDEs and their applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 343-348.
    2. Budhiraja, Amarjit & Lee, Chihoon, 2007. "Long time asymptotics for constrained diffusions in polyhedral domains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1014-1036, August.
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    Cited by:

    1. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.
    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. Hu, Yaozhong & Xi, Yuejuan, 2021. "Estimation of all parameters in the reflected Ornstein–Uhlenbeck process from discrete observations," Statistics & Probability Letters, Elsevier, vol. 174(C).
    4. Hui Jiang & Qingshan Yang, 2022. "Moderate Deviations for Drift Parameter Estimations in Reflected Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1262-1283, June.

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