Pang, Tianxiao and Zhang, Danna and Chong, Terence Tai-Leung
(2013):
*Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Non-stationary Cases.*
Published in: Journal of Time Series Analysis
, Vol. 2, No. 35
(1 March 2014): pp. 133-150.

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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_{t-1}I{t≤k₀}+β₂y_{t-1}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}=1-c/T; and case (II) β₁=β_{1T}=1-c/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 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

Item Type: | MPRA Paper |
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Original Title: | Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Non-stationary 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 - Time-Series 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: | 28 Sep 2019 16:37 |

References: | Andrews, D. W. K. (1987). Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55 (6), 1465-1471. Andrews, D. W. K. and Guggenberger, P. (2008). Asymptotics for stationary very nearly unit root processes. Journal of Time Series Analysis 29 (1), 203-212. Billingsley, P. (1999). Convergence of Probability Measures, 2nd edn. John Wiley and Sons, New York. Chan, N. H. and Wei, C. Z. (1987). Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15 (3), 1050-1063. Chong, T. L. (2001). Structural change in AR(1) models. Econometric Theory 17 (1), 87-155. Csörgő, M., Szyszkowicz, B. and Wang, Q. Y. (2003). Donsker's theorem for self-normalized partial sums processes. Annals of Probability 31 (3), 1228-1240. Feller, W. (1971). An Introduction to Probability Theory and Its Applications. Volume 2. John Wiley and Sons, New York. Giné, E., Götze, F. and Mason, D. M. (1997). When is the Student t-statistic asymptotically standard normal? Annals of Probability 25 (3), 1514-1531. Hansen, B. E. (1992). Tests for parameter instability in regressions with I(1) processes. Journal of Business and Economic Statistics 10 (3), 321-335. Huang, S. H., Pang, T. X. and Weng, C. (2012). Limit theory for moderate deviations from a unit root under innovations with a possibly infinite variance. Methodology and Computing in Applied Probability, forthcoming. Kim, J. and Pollard, D. (1990). Cube root asymptotics. Annals of Statistics 18 (1), 191-219. Mankiw, N. G. and Miron, J. A. (1986). The changing behavior of the term structure of interest rates. Quarterly Journal of Economics 101 (2), 221-228. Mankiw, N. G., Miron, J. A. and Weil, D. N. (1987). The adjustment of expectations to a change in regime: A study of the founding of the Federal Reserve. American Economic Review 77 (3), 358-374. Pang, T. X. and Zhang, D. N. (2011). Asymptotic inferences for an AR(1) model with a change point and possibly infinite variance. Communications in Statistics: Theory and Methods, forthcoming. Pang, T. X., Zhang D. N. and Chong, T. L. (2013). Asymptotic inferences for an AR(1) model with a change point: stationary and nearly non-stationary cases. (Available at http://arxiv.org/abs/1306.1294) Phillips, P. C. B. (1987). Towards a unified asymptotic theory for autoregression. Biometrika 74 (3), 535-547. [color]<LaTeX>\color{red}</LaTeX> Phillips, P. C. B. and Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. Journal of Econometrics 136 (1), 115-130. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/55312 |