Publication Type
Journal Article
Version
acceptedVersion
Publication Date
4-2023
Abstract
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
Keywords
Least squares, Local to unity, Fractional Brownian motion, Fractional Ornstein-Uhlenbeck process
Discipline
Econometrics
Research Areas
Econometrics
Publication
Advances in Econometrics
Volume
45A
First Page
73
Last Page
95
ISSN
0731-9053
Identifier
10.1108/S0731-90532023000045A002
Publisher
Jai Press Inc.
Citation
WANG, Xiaohu; XIAO, Weilin; and Jun YU.
Asymptotic properties of Least Squares Estimator in local to unity processes with fractional Gaussian noises. (2023). Advances in Econometrics. 45A, 73-95.
Available at: https://ink.library.smu.edu.sg/soe_research/2682
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1108/S0731-90532023000045A002