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The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model

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  • Perron, Pierre

Abstract

We tabulate the limiting cumulative distribution and probability density functions of the least-squares estimator in a first-order autoregressive regression when the true model is near-integrated in the sense of Phillips. The results are obtained using an exact numerical method which integrates the appropriate limiting moment generating function. The adequacy of the approximation is examined for various first-order autoregressive processes with a root close to unity.

Suggested Citation

  • Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(02), pages 241-255, August.
  • Handle: RePEc:cup:etheor:v:5:y:1989:i:02:p:241-255_01
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    1. repec:ibn:ijefaa:v:9:y:2017:i:11:p:118-127 is not listed on IDEAS
    2. Abadir, Karim M. & Lucas, Andre, 2004. "A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model," Journal of Econometrics, Elsevier, vol. 119(1), pages 45-71, March.
    3. Marcus J. Chambers, 2015. "The Calculation of Some Limiting Distributions Arising in Near-Integrated Models with GLS Detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 562-586, July.
    4. Pierre Perron & Cosme Vodounou, 2001. "Asymptotic approximations in the near-integrated model with a non-zero initial condition," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-42.
    5. Mukhtar Ali, 2002. "Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 89-119.
    6. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
    7. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    8. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    9. Chambers, MJ & Kyriacou, M, 2016. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Economics Discussion Papers 17623, University of Essex, Department of Economics.
    10. repec:gam:jecnmx:v:6:y:2018:i:1:p:11-:d:134810 is not listed on IDEAS
    11. Aman Ullah & Yong Bao & Yun Wang, 2014. "Exact Distribution of the Mean Reversion Estimator in the Ornstein-Uhlenbeck Process," Working Papers 201413, University of California at Riverside, Department of Economics.
    12. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, EconWPA.
    13. Neil Kellard & Denise Osborn & Jerry Coakley & Marcus J. Chambers, 2015. "Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 630-649, September.
    14. repec:esx:essedp:727 is not listed on IDEAS
    15. Mukhtar M. Ali, 1996. "Exact Distribution of the Least Squares Estimator in a First- Order Autoregressive Model," Econometrics 9604001, EconWPA.
    16. Chambers, MJ, 2016. "The Effects of Sampling Frequency on Detrending Methods for Unit Root Tests," Economics Discussion Papers 16062, University of Essex, Department of Economics.

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