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Distribution of the mean reversion estimator in the Ornstein–Uhlenbeck process

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  • Yong Bao
  • Aman Ullah
  • Yun Wang

Abstract

We derive the exact distribution of the maximum likelihood estimator of the mean reversion parameter (κ) in the Ornstein–Uhlenbeck process using numerical integration through analytical evaluation of a joint characteristic function. Different scenarios are considered: known or unknown drift term, fixed or random start-up value, and zero or positive κ. Monte Carlo results demonstrate the remarkably reliable performance of our exact approach across all the scenarios. In comparison, misleading results may arise under the asymptotic distributions, including the advocated infill asymptotic distribution, which performs poorly in the tails when there is no intercept in the regression and the starting value of the process is nonzero.

Suggested Citation

  • Yong Bao & Aman Ullah & Yun Wang, 2017. "Distribution of the mean reversion estimator in the Ornstein–Uhlenbeck process," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1039-1056, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:1039-1056
    DOI: 10.1080/07474938.2017.1307977
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    Cited by:

    1. Zi‐Yi Guo, 2021. "Out‐of‐sample performance of bias‐corrected estimators for diffusion processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 243-268, March.
    2. Yong Bao & Xiaotian Liu & Aman Ullah, 2020. "On the Exact Statistical Distribution of Econometric Estimators and Test Statistics," Working Papers 202014, University of California at Riverside, Department of Economics, revised Jun 2020.
    3. Jianghao Chu & Tae-Hwy Lee & Aman Ullah & Haifeng Xu, 2020. "Exact Distribution of the F-statistic under Heteroskedasticity of Unknown Form for Improved Inference," Working Papers 202027, University of California at Riverside, Department of Economics.
    4. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2022. "The Grid Bootstrap for Continuous Time Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1390-1402, June.
    5. Emma M. Iglesias & Garry D. A. Phillips, 2020. "Further Results on Pseudo‐Maximum Likelihood Estimation and Testing in the Constant Elasticity of Variance Continuous Time Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 357-364, March.

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