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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1546.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1546.

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Length: 16 pages
Date of creation: Jan 2006
Date of revision:
Publication status: Published in Econometric Theory (June 2008), 24(3): 631-650
Handle: RePEc:cwl:cwldpp:1546

Note: CFP 1243
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
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Cited by:
  1. Yuriy Gorodnichenko & Anna Mikusheva & Serena Ng, 2011. "Estimators for Persistent and Possibly Non-Stationary Data with Classical Properties," NBER Working Papers 17424, National Bureau of Economic Research, Inc.
  2. 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.
  3. 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.
  4. Chirok Han & Peter C.B. Phillips & Donggyu Sul, 2010. "X-Differencing and Dynamic Panel Model Estimation," Cowles Foundation Discussion Papers 1747, Cowles Foundation for Research in Economics, Yale University.

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