IDEAS home Printed from
   My bibliography  Save this article

The limiting distribution of the t-ratio for the unit root test in an AR(1)





We consider the limiting distribution of the t -statistic for testing the random walk hypothesis in the classical Gaussian AR(1) model. Abadir (1995, Econometric Theory, 11, 775­793) derived the first derives a closed (i.e. integration-free) expression for the limit-ing distribution function. This paper derives an alternative closed expression. Abadir¹s and the new expression are valid only for negative arguments and each involve two infinite summa-tions. To enable a numerical treatment, we derive inequalities that allow a suitable truncation of all series occurring in Abadir¹s and the new expression. In both expressions the outer series has a very fast convergence so that truncation after only the first summand usually suffices. The inner series of the new expression displays the numerically desirable Leibnitz property. By differentiating we obtain a new closed expression for the limiting density function. We also find an asymptotic expansion for the lower tail of the limiting distribution function.

Suggested Citation

  • Franz K. Dietrich, 2001. "The limiting distribution of the t-ratio for the unit root test in an AR(1)," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-5.
  • Handle: RePEc:ect:emjrnl:v:4:y:2001:i:2:p:5

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.


    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:ect:emjrnl:v:4:y:2001:i:2:p:5. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: .

    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.