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Structural Change In Nonstationary Ar(1) Models

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  • Pang, Tianxiao
  • Tai-Leung Chong, Terence
  • Zhang, Danna
  • Liang, Yanling

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.

Suggested Citation

  • Pang, Tianxiao & Tai-Leung Chong, Terence & Zhang, Danna & Liang, Yanling, 2018. "Structural Change In Nonstationary Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 34(5), pages 985-1017, October.
  • Handle: RePEc:cup:etheor:v:34:y:2018:i:05:p:985-1017_00
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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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