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Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root


  • Phillips, Peter C.B.
  • Han, Chirok


This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and 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 null rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics , 20, 971–1001). The approach also has useful extensions to dynamic panels.

Suggested Citation

  • Phillips, Peter C.B. & Han, Chirok, 2008. "Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root," Econometric Theory, Cambridge University Press, vol. 24(03), pages 631-650, June.
  • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:631-650_08

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    References listed on IDEAS

    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, 2011. "Uniform Asymptotic Normality In Stationary And Unit Root Autoregression," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1117-1151, December.
    4. 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.
    5. 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.
    6. 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.
    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

    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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