IDEAS home Printed from https://ideas.repec.org/p/boa/wpaper/202527.html
   My bibliography  Save this paper

Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data

Author

Listed:
  • Xiaohu Wang

    (School of Economics, Fudan University, Shanghai, China)

  • Weilin Xiao

    (School of Management, Zhejiang University, Hangzhou, 310058, China)

  • Jun Yu

    (Faculty of Business Administration, University of Macau, Macao, China)

  • Chen Zhang

    (Faculty of Business Administration, University of Macau, Macao, China)

Abstract

This paper first derives two analytic formulae for the autocovariance of the discretely sampled fractional Ornstein-Uhlenbeck (fOU) process. Utilizing the analytic formulae, two main applications are demonstrated: (i) investigation of the accuracy of the likelihood approximation by the Whittle method; (ii) the optimal forecasts with fOU based on discretely sampled data. The finite sample performance of the Whittle method and the derived analytic formula motivate us to introduce a feasible exact maximum likelihood (ML) method to estimate the fOU process. The long-span asymptotic theory of the ML estimator is established, where the convergence rate is a smooth function of the Hurst parameter (i.e., H) and the limiting distribution is always Gaussian, facilitating statistical inference. The asymptotic theory is different from that of some existing estimators studied in the literature, which are discontinuous at H = 3/4 and involve non-standard limiting distributions. The simulation results indicate that the ML method provides more accurate parameter estimates than all the existing methods, and the proposed optimal forecast formula offers a more precise forecast than the existing formula. The fOU process is applied to fit daily realized volatility (RV) and daily trading volume series. When forecasting RVs, it is found that the forecasts generated using the optimal forecast formula together with the ML estimates outperform those generated from all possible combinations of alternative estimation methods and alternative forecast formula.

Suggested Citation

  • Xiaohu Wang & Weilin Xiao & Jun Yu & Chen Zhang, 2025. "Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data," Working Papers 202527, University of Macau, Faculty of Business Administration.
  • Handle: RePEc:boa:wpaper:202527
    as

    Download full text from publisher

    File URL: https://fba.um.edu.mo/wp-content/uploads/RePEc/doc/202527.pdf
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    Fractional Ornstein-Uhlenbeck process; Hurst parameter; Out-of-sample forecast; Maximum likelihood; Whittle likelihood; Composite likelihood;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boa:wpaper:202527. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Carla Leong (email available below). General contact details of provider: https://edirc.repec.org/data/fbmacmo.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.