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Non identification of structural change in non stationary AR(1) models

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  • Tianxiao Pang
  • Terence Tai-Leung Chong
  • Danna Zhang

Abstract

This article studies the identification problem in AR(1) models with a change in the AR parameter 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 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. Two cases were investigated: 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. We derived the limiting distributions of the least squares estimator of the break fraction τ0(=k0/T) for the cases above under some mild conditions. The results showed that the change point τ0 (or k0) is non identifiable for the aforementioned two cases by the least squares method. Monte Carlo experiments were conducted to examine the identification of τ0 under finite sample situations. Our theoretical results are supported by the Monte Carlo experiments.

Suggested Citation

  • Tianxiao Pang & Terence Tai-Leung Chong & Danna Zhang, 2021. "Non identification of structural change in non stationary AR(1) models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(18), pages 4145-4166, August.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:18:p:4145-4166
    DOI: 10.1080/03610926.2019.1711125
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