On the Spectral Density of Fractional Ornstein-Uhlenbeck Processes

Shuping Shi (), Jun Yu and Chen Zhang ()
Additional contact information
Shuping Shi: Macquarie University
Chen Zhang: University of Macau

No 202416, Working Papers from University of Macau, Faculty of Business Administration

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 2 (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, utilising the approximate spectral density, and demonstrate that the AWML estimator exhibits properties of consistency and asymptotic normality when H 2 (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; Realized volatility (search for similar items in EconPapers)
JEL-codes: C13 C22 G10 (search for similar items in EconPapers)
Pages: 60 pages
Date: 2024-08
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in UM-FBA Working Paper Series

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Related works:
Journal Article: On the spectral density of fractional Ornstein–Uhlenbeck processes (2024)
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