IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v21y2000i3p249-260.html
   My bibliography  Save this article

The Limiting Density of Unit Root Test Statistics: A Unifying Technique

Author

Listed:
  • Mithat Gonen
  • Madan L. Puri
  • Frits H. Ruymgaart
  • Martien C. A. Van Zuijlen

Abstract

In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)‐process in a variety of situations. We consider the case of unknown mean and reconsider the well‐known situation where the mean is zero. For long‐range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen‐Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively. AMS 1991 subject classification. Primary 62M10; secondary 62E20.

Suggested Citation

  • Mithat Gonen & Madan L. Puri & Frits H. Ruymgaart & Martien C. A. Van Zuijlen, 2000. "The Limiting Density of Unit Root Test Statistics: A Unifying Technique," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 249-260, May.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:3:p:249-260
    DOI: 10.1111/1467-9892.00184
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00184
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00184?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    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:bla:jtsera:v:21:y:2000:i:3:p:249-260. 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.

    We have no bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.