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Uniform Asymptotic Normality In Stationary And Unit Root Autoregression

Author

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

Abstract

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right|

Suggested Citation

  • 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(6), pages 1117-1151, December.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:06:p:1117-1151_00
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    Cited by:

    1. Ruidong Han & Xinghui Wang & Shuhe Hu, 2018. "Asymptotics of the weighted least squares estimation for AR(1) processes with applications to confidence intervals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 479-490, August.
    2. Joakim Westerlund & Mehdi Hosseinkouchack, 2016. "Modified CADF and CIPS Panel Unit Root Statistics with Standard Chi-squared and Normal Limiting Distributions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 347-364, June.
    3. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1003-1036, October.
    4. Chengwang Liao & Ziwei Mei & Zhentao Shi, 2024. "Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions," Papers 2410.09825, arXiv.org, revised May 2026.
    5. Han, Chirok & Phillips, Peter C.B., 2013. "First difference maximum likelihood and dynamic panel estimation," Journal of Econometrics, Elsevier, vol. 175(1), pages 35-45.
    6. John C. Chao & Peter C. B. Phillips, 2019. "Uniform Inference in Panel Autoregression," Econometrics, MDPI, vol. 7(4), pages 1-28, November.
    7. Phillips, Peter C.B., 2023. "Estimation And Inference With Near Unit Roots," Econometric Theory, Cambridge University Press, vol. 39(2), pages 221-263, April.
    8. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    9. 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.

    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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