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

Xiaohu Wang, Weilin Xiao and Jun Yu

A chapter in Essays in Honor of Joon Y. Park: Econometric Theory, 2023, vol. 45A, pp 73-95 from Emerald Group Publishing Limited

Abstract: This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameterH∈(0,1). It is shown that the estimator is consistent for all values ofH∈(0,1). Moreover, the rate of convergence isn−1whenH∈[0.5,1). The rate of convergence isn−2HwhenH∈(0,0.5). Furthermore, the limiting distribution of the centered LS estimator depends onH. WhenH=0.5, the limiting distribution is the same as that obtained inPhillips (1987a)for the local to unity model with errors for which the standard functional central limit theorem is applicable. WhenH> 0.5 or whenH

Keywords: Least squares; local to unity; fractional Brownian motion; fractional Ornstein–Uhlenbeck process; fitted intercept; functional central limit theorem; C22 (search for similar items in EconPapers)
Date: 2023
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Working Paper: Asymptotic Properties of Least Squares Estimator in Local to Unity Processes with Fractional Gaussian Noises (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-90532023000045a002

DOI: 10.1108/S0731-90532023000045A002

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