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Moment estimators for parameters of Lévy‐driven Ornstein–Uhlenbeck processes

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  • Yanfeng Wu
  • Jianqiang Hu
  • Xiangyu Yang

Abstract

We consider the problem of parameter estimation for Ornstein–Uhlenbeck (OU) processes driven by general Lévy processes. We derive our estimators based on the method of moments and establish a joint central limit theorem for these estimators with explicit formulae for their asymptotic covariance matrix. Numerical experiments are also provided to show that not only our estimators are easy to implement but they are also highly efficient. Our work offers a simple and efficient method to estimate the parameters in Lévy‐driven OU processes.

Suggested Citation

  • Yanfeng Wu & Jianqiang Hu & Xiangyu Yang, 2022. "Moment estimators for parameters of Lévy‐driven Ornstein–Uhlenbeck processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 610-639, July.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:4:p:610-639
    DOI: 10.1111/jtsa.12630
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. Shibin Zhang & Xinsheng Zhang, 2013. "A least squares estimator for discretely observed Ornstein–Uhlenbeck processes driven by symmetric α-stable motions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 89-103, February.
    3. Geurt Jongbloed & Frank H. Van Der Meulen, 2006. "Parametric Estimation for Subordinators and Induced OU Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 825-847, December.
    4. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
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