On the spectral density of fractional Ornstein–Uhlenbeck processes

Shuping Shi, Jun Yu and Chen Zhang

Journal of Econometrics, 2024, vol. 245, issue 1

Abstract: This paper introduces a novel and easy-to-implement method for accurately approximating the spectral density of discretely sampled fractional Ornstein–Uhlenbeck (fOU) processes. The method offers a substantial reduction in approximation error, particularly within the rough region of the fractional parameter H∈(0,0.5). This approximate spectral density has the potential to enhance the performance of estimation methods and hypothesis testing that make use of spectral densities. We introduce the approximate Whittle maximum likelihood (AWML) method for discretely sampled fOU processes, utilizing the approximate spectral density, and demonstrate that the AWML estimator exhibits properties of consistency and asymptotic normality when H∈(0,1), akin to the conventional Whittle maximum likelihood method. Through extensive simulation studies, we show that AWML outperforms existing methods in terms of estimation accuracy in finite samples. We then apply the AWML method to the trading volume of 40 financial assets. Our empirical findings reveal that the estimated Hurst parameters for these assets fall within the range of 0.10 to 0.21, indicating a rough dynamic.

Keywords: Fractional Brownian motion; Fractional Ornstein–Uhlenbeck process; Spectral density; Paxson approximation; Whittle maximum likelihood; Trading volume; Realized volatility (search for similar items in EconPapers)
JEL-codes: C13 C22 G10 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407624002173
Full text for ScienceDirect subscribers only

Related works:
Working Paper: On the Spectral Density of Fractional Ornstein-Uhlenbeck Processes (2024)
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:eee:econom:v:245:y:2024:i:1:s0304407624002173

DOI: 10.1016/j.jeconom.2024.105872

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().