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Asymptotics for Stationary Very Nearly Unit Root Processes

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)
Patrik Guggenberger (Dept. of Economics, UCLA)

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Abstract

This paper considers a mean zero stationary first-order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter rho_n is very near to one in the sense that 1 - rho_n = (n^{-1}).

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File URL: http://cowles.econ.yale.edu/P/cd/d16a/d1607.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1607.

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Length: 8 pages
Date of creation: Mar 2007
Date of revision:
Publication status: Published in Journal of Time Series Analysis (2008), 29(1): 203-210
Handle: RePEc:cwl:cwldpp:1607

Note: CFP 1220.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Asymptotics; Least squares; Nearly nonstationary; Stationary initial condition; Unit root;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07. [Downloadable!] (restricted)
  2. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
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  4. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(1), pages 51-60, 01. [Downloadable!] (restricted)
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  5. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-83, August.
    Other versions:
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This page was last updated on 2009-11-12.

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