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

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  • Perron, P.

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 (1986 A). the Results Are Obtained Using an Exact Numerical Method Which Integrates the Appropriate Limiting Moment Generating Function. the Adequacy of the Approximation Is Examined by Monte Carlo Methods for Various First-Order Autogressive Processes with a Root Close to Unity.

Suggested Citation

  • Perron, P., 1987. "The Calculation of the Limiting Distribution of the Least Squares Estimator in Near-Integrated Model," Cahiers de recherche 8748, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:8748
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    Cited by:

    1. 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.
    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. Yifei Cai, 2018. "Testing the Fisher Effect in the US," Economics Bulletin, AccessEcon, vol. 38(2), pages 1014-1027.
    4. 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.
    5. 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.
    6. 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.
    7. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
    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. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.
    14. 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.
    15. 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.
    16. Ayşe Özge Artekin, 2024. "Testing the Environmental Kuznets Curve Hypothesis within the Context of Industrial Development through NARDL Model: The Case of France," International Journal of Energy Economics and Policy, Econjournals, vol. 14(5), pages 401-409, September.
    17. repec:esx:essedp:727 is not listed on IDEAS
    18. Mukhtar M. Ali, 1996. "Exact Distribution of the Least Squares Estimator in a First- Order Autoregressive Model," Econometrics 9604001, University Library of Munich, Germany.
    19. 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.
    20. 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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    Keywords

    Econometric Models ; Time Series;

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