ASYMPTOTIC INFERENCES FOR AN AR(1) MODEL WITH A CHANGE POINT: STATIONARY AND NEARLY NON-STATIONARY CASES

Authors

  • Tianxiao Pang,

    Corresponding author
    1. Department of Mathematics, Yuquan Campus, Zhejiang University, Hangzhou, China
    • Correspondence to: Tianxiao Pang, Department of Mathematics, Yuquan Campus, Zhejiang University, Hangzhou 310027, China. E-mail: txpang@zju.edu.cn

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  • Danna Zhang,

    1. Department of Mathematics, Yuquan Campus, Zhejiang University, Hangzhou, China
    2. Department of Statistics, University of Chicago, Chicago, IL, USA
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  • Terence Tai-Leung Chong

    1. Department of Economics and Institute of Global Economics and Finance, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
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Abstract

This article examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter β near the unity at an unknown time k0. Consider the model yt = β1yt − 1I{t ≤ k0} + β2yt − 1I{t > k0} + ϵt, t = 1,2, … ,T, where I{ ⋅ } denotes the indicator function. We examine two cases: case I | β1 | < 1,β2 = β2T = 1 − c ∕ T; and case II β1 = β1T = 1 − c ∕ T, | β2 | < 1, where c is a fixed constant, and {ϵt,t ≥ 1} is a sequence of i.i.d. random variables, which are in the domain of attraction of the normal law with zero means and possibly infinite variances. We derive the limiting distributions of the least squares estimators of β1 and β2 and that of the break-point estimator for shrinking break for the aforementioned cases. Monte Carlo simulations are conducted to demonstrate the finite-sample properties of the estimators. Our theoretical results are supported by Monte Carlo simulations.

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