Asymptotic properties of least squares estimator in local to unity processes with fractional Gaussian noises

• Main Authors: WANG, Xiaohu, XIAO, Weilin, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Least squares; Local to unity; Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2458; https://ink.library.smu.edu.sg/context/soe_research/article/3457/viewcontent/FOU08_.pdf
• Institution: Singapore Management University

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. It is shown that the estimator is consistent when H ∈ (0, 1). Moreover, the rate of convergence is n when H ∈ [0.5, 1). The rate of convergence is n2H when H ∈ (0, 0.5). Furthermore, the limit distribution of the centered least squares estimator depends on H. When H = 0.5, the limit distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central theorem is applicable. When H > 0.5 or when H < 0.5, the limit distributions are new to the literature. Simulation studies are performed to check the reliability of the asymptotic approximation for di§erent values of sample size.