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Maximum Likelihood Estimation for the Fractional Vasicek Model

Author

Listed:
  • Katsuto Tanaka

    (Gakushuin University)

  • Weilin Xiao

    (Zhejiang University)

  • Jun Yu

    (School of Economics and Lee Kong Chian School of Business, Singapore Management University)

Abstract

This paper is concerned about the problem of estimating the drift parameters in the fractional Vasicek model from a continuous record of observations. Based on the Girsanov theorem for the fractional Brownian motion, the maximum likelihood (ML) method is used. The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the null recurrent case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter will change the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.

Suggested Citation

  • Katsuto Tanaka & Weilin Xiao & Jun Yu, 2019. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Economics and Statistics Working Papers 8-2019, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2019_008
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    Cited by:

    1. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    2. Rachid Belfadli & Khalifa Es-Sebaiy & Fatima-Ezzahra Farah, 2022. "Statistical analysis of the non-ergodic fractional Ornstein–Uhlenbeck process with periodic mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 885-911, October.
    3. Chao Wei, 2024. "Least squares estimation for a class of uncertain Vasicek model and its application to interest rates," Statistical Papers, Springer, vol. 65(4), pages 2441-2459, June.
    4. Kohei Chiba, 2020. "An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 319-353, July.
    5. Khalifa Es-Sebaiy & Mohammed Es.Sebaiy, 2021. "Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 409-436, June.

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    Keywords

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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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