Asymptotic Properties of Least Squares Estimator in Local to Unity Processes with Fractional Gaussian Noises

Xiaohu Wang (), Weilin Xiao () and Jun Yu
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Xiaohu Wang: Fudan University
Weilin Xiao: Zhejiang University

No 27-2020, Economics and Statistics Working Papers from Singapore Management University, School of Economics

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. 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

Keywords: Least squares; Local to unity; Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2020-12-23
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Chapter: Asymptotic Properties of the Least Squares Estimator in Local to Unity Processes with Fractional Gaussian Noise (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:ris:smuesw:2020_027

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