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

Tianxiao Pang, Terence Tai Leung Chong and Danna Zhang

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 18, 4145-4166

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.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2019.1711125 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:50:y:2021:i:18:p:4145-4166

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2019.1711125

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().