On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison

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...

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Main Authors: SHI, Shuping, Jun YU, ZHANG, Chen
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Language:English
Published: Institutional Knowledge at Singapore Management University 2023
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Online Access:https://ink.library.smu.edu.sg/soe_research/2680
https://ink.library.smu.edu.sg/context/soe_research/article/3679/viewcontent/Paxson_approximation_fOU08__2_.pdf
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spelling sg-smu-ink.soe_research-36792023-07-14T05:49:59Z On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison SHI, Shuping Jun YU, ZHANG, Chen 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. 2023-05-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2680 https://ink.library.smu.edu.sg/context/soe_research/article/3679/viewcontent/Paxson_approximation_fOU08__2_.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Fractional Brownian motion; fractional Ornstein-Uhlenbeck process; spectral density; Paxson approximation; Whittle likelihood; Realized volatility Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Fractional Brownian motion; fractional Ornstein-Uhlenbeck process; spectral density; Paxson approximation; Whittle likelihood; Realized volatility
Econometrics
spellingShingle Fractional Brownian motion; fractional Ornstein-Uhlenbeck process; spectral density; Paxson approximation; Whittle likelihood; Realized volatility
Econometrics
SHI, Shuping
Jun YU,
ZHANG, Chen
On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
description 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.
format text
author SHI, Shuping
Jun YU,
ZHANG, Chen
author_facet SHI, Shuping
Jun YU,
ZHANG, Chen
author_sort SHI, Shuping
title On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
title_short On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
title_full On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
title_fullStr On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
title_full_unstemmed On the spectral density of fractional Ornstein-Uhlenbeck Process: Approximation, Estimation, and Model Comparison
title_sort on the spectral density of fractional ornstein-uhlenbeck process: approximation, estimation, and model comparison
publisher Institutional Knowledge at Singapore Management University
publishDate 2023
url https://ink.library.smu.edu.sg/soe_research/2680
https://ink.library.smu.edu.sg/context/soe_research/article/3679/viewcontent/Paxson_approximation_fOU08__2_.pdf
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