Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process

Xiaohu Wang, Weilin Xiao and Jun Yu

Journal of Econometrics, 2023, vol. 232, issue 2, 389-415

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 H, 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 (search for similar items in EconPapers)
JEL-codes: C15 C22 C32 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:232:y:2023:i:2:p:389-415

DOI: 10.1016/j.jeconom.2021.08.001

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