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Gaussian Inference in AR(1) Time Series with or without a Unit Root

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Abstract

This note introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite sample bias, are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform vn rate of convergence. En route, a useful CLT for sample covariances of linear processes is given, following Phillips and Solo (1992). The approach also has useful extensions to dynamic panels.

Suggested Citation

  • Peter C. B. Phillips & Chirok Han, 2006. "Gaussian Inference in AR(1) Time Series with or without a Unit Root," Cowles Foundation Discussion Papers 1546, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1546
    Note: CFP 1243
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    References listed on IDEAS

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    1. 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.
    2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1003-1036, October.
    2. Peter C.B. Phillips & Chirok Han, 2014. "True Limit Distributions of the Anderson-Hsiao IV Estimators in Panel Autoregression," Cowles Foundation Discussion Papers 1963, Cowles Foundation for Research in Economics, Yale University.
    3. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2014. "X-Differencing And Dynamic Panel Model Estimation," Econometric Theory, Cambridge University Press, vol. 30(01), pages 201-251, February.
    4. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2011. "Uniform Asymptotic Normality In Stationary And Unit Root Autoregression," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1117-1151, December.
    5. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    6. Phillips, Peter C.B. & Han, Chirok, 2015. "The true limit distributions of the Anderson–Hsiao IV estimators in panel autoregression," Economics Letters, Elsevier, vol. 127(C), pages 89-92.
    7. Jhih-Gang Chen & Biing-Shen Kuo, 2013. "Gaussian inference in general AR(1) models based on difference," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 447-453, July.
    8. In Choi, 2016. "Cross-sectional maximum likelihood and bias-corrected pooled least squares estimators for dynamic panels with short T," Working Papers 1610, Research Institute for Market Economy, Sogang University.

    More about this item

    Keywords

    Autoregression; Differencing; Gaussian limit; Mildly explosive processes; Uniformity; Unit root;

    JEL classification:

    • 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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