Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises

This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H 2 (0; 1). It is shown that the estimator is consistent for all values of H 2 (0; 1). Moreover, t...

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Main Authors: WANG, Xiaohu, XIAO, Weilin, Jun YU
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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/2682
https://ink.library.smu.edu.sg/context/soe_research/article/3681/viewcontent/FOU08_.pdf
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spelling sg-smu-ink.soe_research-36812023-08-11T06:49:34Z Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises WANG, Xiaohu XIAO, Weilin Jun YU, This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H 2 (0; 1). It is shown that the estimator is consistent for all values of H 2 (0; 1). Moreover, the rate of convergence is n 1 when H 2 [0:5; 1). The rate of convergence is n 2H when H 2 (0; 0:5). Furthermore, the limiting distribution of the centered least squares estimator depends on H. When H = 0:5, the limiting distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central limit theorem is applicable. When H > 0:5 or when H 2023-04-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2682 info:doi/10.1108/S0731-90532023000045A002 https://ink.library.smu.edu.sg/context/soe_research/article/3681/viewcontent/FOU08_.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Least squares Local to unity Fractional Brownian motion Fractional Ornstein-Uhlenbeck process Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Least squares
Local to unity
Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Econometrics
spellingShingle Least squares
Local to unity
Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Econometrics
WANG, Xiaohu
XIAO, Weilin
Jun YU,
Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
description This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H 2 (0; 1). It is shown that the estimator is consistent for all values of H 2 (0; 1). Moreover, the rate of convergence is n 1 when H 2 [0:5; 1). The rate of convergence is n 2H when H 2 (0; 0:5). Furthermore, the limiting distribution of the centered least squares estimator depends on H. When H = 0:5, the limiting distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central limit theorem is applicable. When H > 0:5 or when H
format text
author WANG, Xiaohu
XIAO, Weilin
Jun YU,
author_facet WANG, Xiaohu
XIAO, Weilin
Jun YU,
author_sort WANG, Xiaohu
title Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
title_short Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
title_full Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
title_fullStr Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
title_full_unstemmed Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises
title_sort asymptotic properties of least squares estimator in local to unity processes with fractional gaussian noises
publisher Institutional Knowledge at Singapore Management University
publishDate 2023
url https://ink.library.smu.edu.sg/soe_research/2682
https://ink.library.smu.edu.sg/context/soe_research/article/3681/viewcontent/FOU08_.pdf
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