IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i1p27-34.html
   My bibliography  Save this article

Remark on the asymptotic distribution of the OLS estimator in a simple Gaussian unit-root autoregression

Author

Listed:
  • Vougas, Dimitrios V.

Abstract

This paper considers the asymptotic distribution of the OLS estimator in a simple, Gaussian unit-root AR(1) with fixed, non-zero startup. All asymptotic possibilities are considered. The approach is new, relatively simple, and relies on observing and determining the asymptotic/limiting behavior of the underlying finite sample distribution. It does not rely on inversion of joint moment generating or characteristic functions to derive limiting distributions. The paper introduces small-sigma/parameter-based asymptotic theory and re-examines large-sample asymptotic theory. In addition, combinations of these asymptotic approaches are considered explicitly. The analysis provides a set of very interesting and sometimes surprising results.

Suggested Citation

  • Vougas, Dimitrios V., 2006. "Remark on the asymptotic distribution of the OLS estimator in a simple Gaussian unit-root autoregression," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 27-34, January.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:27-34
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00263-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Forchini, G., 2002. "The Exact Cumulative Distribution Function Of A Ratio Of Quadratic Forms In Normal Variables, With Application To The Ar(1) Model," Econometric Theory, Cambridge University Press, vol. 18(4), pages 823-852, August.
    2. Abadir, Karim M & Hadri, Kaddour, 2000. "Is More Information a Good Thing? Bias Nonmonotonicity in Stochastic Difference Equations," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 91-100, April.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(1), pages 62-80, January.
    5. Abadir, Karim M., 1993. "Ols Bias in a Nonstationary Autoregression," Econometric Theory, Cambridge University Press, vol. 9(1), pages 81-93, January.
    6. Kiviet, Jan F & Phillips, Garry D A, 1992. "Exact Similar Tests for Unit Roots and Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 349-367, August.
    7. Satchell, Stephen Ellwood, 1984. "Approximation to the Finite Sample Distribution for Nonstable First Order Stochastic Difference Equations," Econometrica, Econometric Society, vol. 52(5), pages 1271-1289, September.
    8. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Atukorala, Ranjani & Sriananthakumar, Sivagowry, 2015. "A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information," Economic Modelling, Elsevier, vol. 45(C), pages 169-174.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aman Ullah & Yong Bao & Ru Zhang, 2014. "Moment Approximation for Unit Root Models with Nonnormal Errors," Working Papers 201401, University of California at Riverside, Department of Economics.
    2. Lawford, Steve & Stamatogiannis, Michalis P., 2009. "The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators," Journal of Econometrics, Elsevier, vol. 148(2), pages 124-130, February.
    3. J. Roderick McCrorie, 2021. "Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 244-281, November.
    4. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.
    5. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    6. Faff, Robert & Gray, Philip, 2006. "On the estimation and comparison of short-rate models using the generalised method of moments," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3131-3146, November.
    7. Magnus, J.R. & Pesaran, B., 1990. "Forecasting, misspecification and unit roots : The case of Ar(1) versus ARMA(1,1)," Discussion Paper 1990-2, Tilburg University, Center for Economic Research.
    8. Ralf Ostermark & Rune Hoglund, 1999. "Simulating competing cointegration tests in a bivariate system," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 831-846.
    9. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.
    10. Abadir, Karim M. & Lucas, Andre, 2000. "Quantiles for t-statistics based on M-estimators of unit roots," Economics Letters, Elsevier, vol. 67(2), pages 131-137, May.
    11. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
    12. Jorion, Philippe & Sweeney, Richard J., 1996. "Mean reversion in real exchange rates: evidence and implications for forecasting," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 535-550, August.
    13. Mukhtar M. Ali, 1996. "Exact Distribution of the Least Squares Estimator in a First- Order Autoregressive Model," Econometrics 9604001, University Library of Munich, Germany.
    14. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    15. Ferretti, Nélida, 1993. "Bootstrap tests for unit root AR(1) models," DES - Working Papers. Statistics and Econometrics. WS 3733, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    17. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
    18. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    19. Kourogenis, Nikolaos & Pittis, Nikitas & Samartzis, Panagiotis, 2024. "Unbounded heteroscedasticity in autoregressive models," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    20. Jürgen Wolters & Uwe Hassler, 2006. "Unit Root Testing," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 4, pages 41-56, Springer.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:27-34. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.