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Maximum Likelihood Estimation for the Fractional Vasicek Model

Author

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  • Katsuto Tanaka

    (Faculty of Economics, Gakushuin University, Tokyo 171-8588, Japan
    We would like to thank three referees for helpful comments. Jun Yu’s homepage http://www.mysmu.edu/faculty/yujun/ .)

  • Weilin Xiao

    (School of Management, Zhejiang University, Hangzhou 310058, China
    We would like to thank three referees for helpful comments. Jun Yu’s homepage http://www.mysmu.edu/faculty/yujun/ .)

  • Jun Yu

    (School of Economics and Lee Kong Chian Schoo of Business, Singapore Management University, Singapore 178903, Singapore
    We would like to thank three referees for helpful comments. Jun Yu’s homepage http://www.mysmu.edu/faculty/yujun/ .)

Abstract

This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary 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 changes 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, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:3:p:32-:d:397839
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    References listed on IDEAS

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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. 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.
    4. 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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    More about this item

    Keywords

    maximum likelihood estimate; fractional Vasicek model; asymptotic distribution; stationary process; explosive process; boundary process;
    All these keywords.

    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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