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Asymptotics for stationary very nearly unit root processes

Author

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  • Donald W. K. Andrews
  • Patrik Guggenberger

Abstract

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 ρn is very near to one in the sense that 1 − ρn = o(n−1).

Suggested Citation

  • Donald W. K. Andrews & Patrik Guggenberger, 2008. "Asymptotics for stationary very nearly unit root processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 203-212, January.
  • Handle: RePEc:bla:jtsera:v:29:y:2008:i:1:p:203-212
    DOI: 10.1111/j.1467-9892.2007.00552.x
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    File URL: https://doi.org/10.1111/j.1467-9892.2007.00552.x
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    References listed on IDEAS

    as
    1. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
    2. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    3. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    4. 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.
    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. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Tianxiao Pang & Danna Zhang & Terence Tai-Leung Chong, 2014. "Asymptotic Inferences For An Ar(1) Model With A Change Point: Stationary And Nearly Non-Stationary Cases," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 133-150, March.
    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. 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.
    4. Jardet, Caroline & Monfort, Alain & Pegoraro, Fulvio, 2013. "No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 389-402.
    5. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    6. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    7. repec:eee:dyncon:v:90:y:2018:i:c:p:343-365 is not listed on IDEAS
    8. Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Marina (Турунцева, Марина), 2017. "Testing the Hypothesis of a Unit Root for Independent Panels
      [Тестирование Гипотезы О Наличии Единичного Корня Для Независимых Панелей]
      ," Working Papers 021707, Russian Presidential Academy of National Economy and Public Administration.

    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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