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

Xiaohu Wang, Weilin Xiao (), Jun Yu and Chen Zhang ()
Additional contact information
Xiaohu Wang: School of Economics, Fudan University, Shanghai, China
Weilin Xiao: School of Management, Zhejiang University, Hangzhou, 310058, China
Chen Zhang: Faculty of Business Administration, University of Macau, Macao, China

No 202527, Working Papers from University of Macau, Faculty of Business Administration

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.

Keywords: Fractional Ornstein-Uhlenbeck process; Hurst parameter; Out-of-sample forecast; Maximum likelihood; Whittle likelihood; Composite likelihood (search for similar items in EconPapers)
JEL-codes: C15 C22 C32 (search for similar items in EconPapers)
Pages: 57 pages
Date: 2025-03
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in UM-FBA Working Paper Series

Downloads: (external link)
https://fba.um.edu.mo/wp-content/uploads/RePEc/doc/202527.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:boa:wpaper:202527

Access Statistics for this paper

More papers in Working Papers from University of Macau, Faculty of Business Administration Contact information at EDIRC.
Bibliographic data for series maintained by Carla Leong ().