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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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 |
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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 |
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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 |
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text |
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WANG, Xiaohu XIAO, Weilin Jun YU, |
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WANG, Xiaohu XIAO, Weilin Jun YU, |
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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 |
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Institutional Knowledge at Singapore Management University |
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2023 |
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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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