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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.

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  • 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(2), pages 241-255, August.
    • Handle: RePEc:cup:etheor:v:5:y:1989:i:02:p:241-255_01
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    Cited by:

    1. 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.
    2. Lin Liu & Kai Shi, 2017. "A Comparative Analysis on the Wealth Effect between in the Stock Market and in the Housing Market in China," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(11), pages 118-127, November.
    3. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.
    4. 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.
    5. 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.
    6. K. Maekawa & J. L. Knight & H. Hisamatsu, 1998. "Finite sample comparisons of the distributions of the ols and gls estimators in regression with an integrated regsorad correlated errors," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 387-413.
    7. 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.
    8. 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.
    9. Yifei Cai, 2018. "Testing the Fisher Effect in the US," Economics Bulletin, AccessEcon, vol. 38(2), pages 1014-1027.
    10. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.
    11. 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.
    12. Erdal Dursun, 2022. "The Nexus among Civil Aviation, Energy Performance Efficiency and GDP in terms of Ecological Footprint: Evidence from France and Finland," International Journal of Energy Economics and Policy, Econjournals, vol. 12(5), pages 243-251, September.
    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 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.
    16. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
    17. Mukhtar M. Ali, 1996. "Exact Distribution of the Least Squares Estimator in a First- Order Autoregressive Model," Econometrics 9604001, University Library of Munich, Germany.
    18. Erdal Dursun, 2022. "Investigating the Air Transport-Induced EKC Hypothesis: Evidence from NAFTA Countries," International Journal of Energy Economics and Policy, Econjournals, vol. 12(4), pages 494-500, July.
    19. 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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