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Estimation of all parameters in the reflected Ornstein–Uhlenbeck process from discrete observations

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  • Hu, Yaozhong
  • Xi, Yuejuan

Abstract

Assuming that a reflected Ornstein–Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate all the drift and diffusion parameters via the celebrated ergodic theorem. With the sampling time step h>0 arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sampling size n tends to infinity. This provides a complete solution to an open problem left in Hu et al. (2015).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000614
    DOI: 10.1016/j.spl.2021.109099
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    References listed on IDEAS

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    1. 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.
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