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Asymptotic Inferences For An Ar(1) Model With A Change Point: Stationary And Nearly Non-Stationary Cases

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

Abstract

type="main" xml:id="jtsa12055-abs-0001"> 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 k 0 . Consider the model y t = β 1 y t − 1 I{t ≤ k 0 } + β 2 y t − 1 I{t > k 0 } + ϵ t , t = 1,2, … ,T, where I{ ⋅ } denotes the indicator function. We examine two cases: case I &7C β 1 &7C > 1,β 2 = β 2T = 1 − c ∕ T; and case II β 1 = β 1T = 1 − c ∕ T, &7C β 2 &7C > 1, where c is a fixed constant, and {ϵ t ,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 β 1 and β 2 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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  • Tianxiao Pang & Danna Zhang & Terence Tai-Leung Chong, 2014. "Asymptotic Inferences For An Ar(1) Model With A Change Point: Stationary And Nearly Non-Stationary Cases," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 133-150, March.
  • Handle: RePEc:bla:jtsera:v:35:y:2014:i:2:p:133-150
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    File URL: http://hdl.handle.net/10.1111/jtsa.12055
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    References listed on IDEAS

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    1. Chong, Terence Tai-Leung, 2001. "Structural Change In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 17(1), pages 87-155, February.
    2. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    3. Mankiw, N Gregory & Miron, Jeffrey A & Weil, David N, 1987. "The Adjustment of Expectations to a Change in Regime: A Study of the Founding of the Federal Reserve," American Economic Review, American Economic Association, vol. 77(3), pages 358-374, June.
    4. Donald W. K. Andrews & Patrik Guggenberger, 2008. "Asymptotics for stationary very nearly unit root processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 203-212, January.
    5. N. Gregory Mankiw & Jeffrey A. Miron, 1986. "The Changing Behavior of the Term Structure of Interest Rates," The Quarterly Journal of Economics, Oxford University Press, vol. 101(2), pages 211-228.
    6. Pang, Tianxiao & Zhang, Danna & Chong, Terence Tai-Leung, 2013. "Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Non-stationary Cases," MPRA Paper 55312, University Library of Munich, Germany.
    7. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
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    Cited by:

    1. 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.
    2. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.

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