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<p>In this paper, we study asymptotic properties of the Yule-Walker estimator and ordinary least squares (OLS) estimator in a mildly stable unit root process with Gaussian noise. By the change of measure method and asymptotic analysis technique, we establish the exponential nonuniform Berry-Esseen bounds of the two estimators. As applications, the optimal uniform Berry-Esseen bounds and optimal Cramér-type moderate deviation principles can be obtained.</p>

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Asymptotic Properties of the Estimators in Mildly Stable Unit Root Process

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Xiyao Zhang,
  • Hui Jiang,
  • Weilin Xiao,
  • Weigang Wang

摘要

In this paper, we study asymptotic properties of the Yule-Walker estimator and ordinary least squares (OLS) estimator in a mildly stable unit root process with Gaussian noise. By the change of measure method and asymptotic analysis technique, we establish the exponential nonuniform Berry-Esseen bounds of the two estimators. As applications, the optimal uniform Berry-Esseen bounds and optimal Cramér-type moderate deviation principles can be obtained.