Pang, Tianxiao and Zhang, Danna and Chong, Terence TaiLeung (2013): Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Nonstationary Cases. Published in: Journal of Time Series Analysis , Vol. 2, No. 35 (1. March 2014): pp. 133150.

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Abstract
This paper 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 k₀. Consider the model y_{t}=β₁y_{t1}I{t≤k₀}+β₂y_{t1}I{t>k₀}+ε_{t}, t=1,2,⋯,T, where I{⋅} denotes the indicator function. We examine two cases: Case (I) β₁<1,β₂=β_{2T}=1c/T; and case (II) β₁=β_{1T}=1c/T,β₂<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 β₁ and β₂, and that of the breakpoint 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
Item Type:  MPRA Paper 

Original Title:  Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Nonstationary Cases 
Language:  English 
Keywords:  AR(1) model, Change point, Domain of attraction of the normal law, Limiting distribution, Least squares estimator. 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  55312 
Depositing User:  Terence T L Chong 
Date Deposited:  16. Apr 2014 03:47 
Last Modified:  16. Apr 2014 04:37 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/55312 