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

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  • Wang, Xiaohu

    (Fudan University)

  • Xiao, Weilin

    (Zhejiang University)

  • Yu, Jun

    (School of Economics, Singapore Management University)

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

Suggested Citation

  • Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2020. "Asymptotic Properties of Least Squares Estimator in Local to Unity Processes with Fractional Gaussian Noises," Economics and Statistics Working Papers 27-2020, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2020_027
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    Keywords

    Least squares; Local to unity; Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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