IDEAS home Printed from https://ideas.repec.org/p/dkn/ecomet/fe_2014_03.html
   My bibliography  Save this paper

On the Asymptotic Distribution of the DF�GLS Test Statistic

Author

Listed:
  • Joakim Westerlund

    () (Deakin University)

Abstract

In a very influential paper Elliott et al. (Efficient Tests for an Autoregressive Unit Root, Econometrica 64, 813�836, 1996) show that no uniformly most powerful test for the unit root testing problem exits, derive the relevant power envelope and characterize a family of point-optimal tests. As a by-product, they also propose a �GLS detrended� version of the conventional Dickey�Fuller test, denoted DF�GLS, that has since then become very popular among practitioners, much more so than the point-optimal tests. In view of this, it is quite strange to find that, while conjectured in Elliott et al. (1996), so far there seems to be no formal proof of the asymptotic distribution of the DF�GLS test statistic. By providing three separate proofs the current paper not only substantiates the required result, but also provides insight regarding the pros and cons of different methods of proof.

Suggested Citation

  • Joakim Westerlund, "undated". "On the Asymptotic Distribution of the DF�GLS Test Statistic," Financial Econometics Series 2014_03, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  • Handle: RePEc:dkn:ecomet:fe_2014_03
    as

    Download full text from publisher

    File URL: http://www.deakin.edu.au/buslaw/aef/workingpapers/fin-econometrics/2014_03.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Hashem Pesaran, M. & Yamagata, Takashi, 2008. "Testing slope homogeneity in large panels," Journal of Econometrics, Elsevier, vol. 142(1), pages 50-93, January.
    2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    3. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    4. Maurice J.G. Bun, 2004. "Testing poolability in a system of dynamic regressions with nonspherical disturbances," Empirical Economics, Springer, vol. 29(1), pages 89-106, January.
    5. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Unit root test; GLS detrending; Asymptotic distribution; Asymptotic local power; Method of proof.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:dkn:ecomet:fe_2014_03. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr Susan S Sharma). General contact details of provider: http://edirc.repec.org/data/bsdeaau.html .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.