Publication Type
Journal Article
Version
submittedVersion
Publication Date
2-2023
Abstract
This paper proposes to model and forecast realized volatility (RV) using the fractional Ornstein-Uhlenbeck (fO-U) process with a general Hurst parameter, H. A two-stage method is introduced for estimating parameters in the fO-U process based on discrete-sampled observations. In the first stage, H is estimated based on the ratio of two second-order differences of observations from different frequencies. In the second stage, with the estimated , the other parameters of the model are estimated by the method of moments. All estimators have closed-form expressions and are easy to implement. A large sample theory of the proposed estimators is derived. Extensive simulations show that the proposed estimators and the large-sample theory perform well in finite samples. We apply the model and the method to the logarithmic daily RV series of various financial assets. Our empirical findings suggest that H is much smaller than 1/2, indicating that the RV series have rough sample paths, and that the mean reversion parameter takes a small positive number, indicating that the RV series are stationary but have slow mean reversion. The proposed model is compared with many alternative models, including the fractional Brownian motion, ARFIMA, and HAR, in forecasting RV and logarithmic RV.
Keywords
Rough volatility, Fractional Ornstein-Uhlenbeck process, Hurst parameter, Long memory, Anti-persistent errors, Out-of-sample forecasting, ARFIMA
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
232
Issue
2/3
First Page
389
Last Page
415
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2021.08.001
Publisher
Elsevier
Citation
WANG, Xiaohu; XIAO, Weilin; and Jun YU.
Modeling and forecasting realized volatility with the fractional Ornstein-Uhlenbeck process. (2023). Journal of Econometrics. 232, (2/3), 389-415.
Available at: https://ink.library.smu.edu.sg/soe_research/2592
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.jeconom.2021.08.001