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Asymptotics for stationary very nearly unit root processes

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  • Donald W. K. Andrews
  • Patrik Guggenberger

Abstract

This article 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 = o(n-super- - 1). Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 29 (2008)
Issue (Month): 1 (01)
Pages: 203-212

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Handle: RePEc:bla:jtsera:v:29:y:2008:i:1:p:203-212

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  1. 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.
  2. L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
  3. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  4. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
  5. 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.
  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. 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.
  2. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
  3. 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.
  4. 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.
  5. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
  6. 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.

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