On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison - SHI, Shuping (Institutional Knowledge at Singapore Management University, 2023)
This paper introduces a novel method for accurately approximating the spectral density of the discretely-sampled fractional Ornstein-Uhlenbeck (fOU) process. We utilize this approximated spec-tral density to develop an estimation method called the approximated Whittle maximum likelihood method (AWML) for fOU. Additionally, we develop a likelihood-ratio (LR) test using the approxi-mated spectral densities to distinguish between the fractional Brownian motion (fBm) and fOU pro-cesses, two popular models in the volatility literature. Simulation studies demonstrate that the AWML method improves the estimation speed and accuracy compared to existing ones and that the LR test is effective in distinguishing between the two processes when deviations are moderate. We then apply the AWML method and the LR test to the log realized volatility of 40 financial assets. Our findings reveal that the estimated Hurst parameters for these assets fall within the range of 0.10 to 0.23, in-dicating a rough volatility dynamic. Moreover, our LR test results suggest that both fBm and fOU are empirically relevant, with some financial assets favoring fBm and others leaning towards fOU. The proposed LR test can provide valuable guidance for selecting an appropriate model in empirical applications.