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STRUCTURAL CHANGE IN NONSTATIONARY AR(1) MODELS

Published online by Cambridge University Press:  24 July 2017

Tianxiao Pang ,
Terence Tai-Leung Chong ,
Danna Zhang  and
Yanling Liang
Tianxiao Pang*
Affiliation:
Zhejiang University
Terence Tai-Leung Chong
Affiliation:
The Chinese University of Hong Kong Nanjing University
Danna Zhang
Affiliation:
University of California
Yanling Liang
Affiliation:
Zhejiang University
*
*Address correspondence to Tianxiao Pang, School of Mathematical Sciences, Yuquan Campus, Zhejiang University, Hangzhou 310027, P.R. China; e-mail: txpang@zju.edu.cn.
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Abstract

This article revisits the asymptotic inference for nonstationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k0. Consider the model ${y_t} = {\beta _1}{y_{t - 1}}I\{ t \le {k_0}\} + {\beta _2}{y_{t - 1}}I\{ t > {k_0}\} + {\varepsilon _t},t = 1,2, \ldots ,T$, where I{·} denotes the indicator function, one of ${\beta _1}$ and ${\beta _2}$ depends on the sample size T, and the other is equal to one. We examine four cases: Case (I): ${\beta _1} = {\beta _{1T}} = 1 - c/{k_T}$, ${\beta _2} = 1$; (II): ${\beta _1} = 1$, ${\beta _2} = {\beta _{2T}} = 1 - c/{k_T}$; (III): ${\beta _1} = 1$, ${\beta _2} = {\beta _{2T}} = 1 + c/{k_T}$; and case (IV): ${\beta _1} = {\beta _{1T}} = 1 + c/{k_T}$, ${\beta _2} = 1$, where c is a fixed positive constant, and kT is a sequence of positive constants increasing to ∞ such that kT = o(T). We derive the limiting distributions of the t-ratios of ${\beta _1}$ and ${\beta _2}$ and the least squares estimator of the change point for the cases above under some mild conditions. Monte Carlo simulations are conducted to examine the finite-sample properties of the estimators. Our theoretical findings are supported by the Monte Carlo simulations.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 5 , October 2018 , pp. 985 - 1017
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

Tianxiao Pang and Yanling Liang’s research was supported by the Department of Education of Zhejiang Province in China (N20140202).

References

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