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Asymptotics for Stationary Very Nearly Unit Root Processes

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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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, 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: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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References

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  1. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
  2. 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.
  3. 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.
  4. Liudas Giraitis & Peter C.B. Phillips, 2004. "Uniform Limit Theory for Stationary Autoregression," Cowles Foundation Discussion Papers 1475, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. 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.
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Cited by:
  1. Guillaume Chevillon & Sophocles Mavroeidis, 2013. "Learning generates Long Memory," Post-Print hal-00661012, HAL.
  2. Pang, Tianxiao & Zhang, Danna & Chong, Terence Tai-Leung, 2013. "Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Non-stationary Cases," MPRA Paper 55312, University Library of Munich, Germany.
  3. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
  4. Caroline JARDET & Alain MONFORT & Fulvio PEGORARO, 2011. "No-arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth," Working Papers 2011-03, Centre de Recherche en Economie et Statistique.
  5. Joakim Westerlund, . "Pooled Panel Unit Root Tests and the Effect of Past Initialization," Financial Econometics Series 2014_06, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  6. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers 13-02, Ohio State University, Department of Economics.

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