IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v70y2002i5p1963-2006.html
   My bibliography  Save this article

A Fractional Dickey-Fuller Test for Unit Roots

Author

Listed:
  • Juan J. Dolado

    () (Universidad Carlos III de Madrid, Spain)

  • Jesus Gonzalo

    () (Universidad Carlos III de Madrid, Spain)

  • Laura Mayoral

    () (Universitat Autonoma de Barcelona, Spain)

Abstract

This paper presents a new test for fractionally integrated ("FI") processes. In particular, we propose a testing procedure in the time domain that extends the well-known Dickey-Fuller approach, originally designed for the "I"(1) versus "I"(0) case, to the more general setup of "FI"("d"-sub-0) versus "FI"("d"-sub-1), with "d"-sub-1<"d"-sub-0. When "d"-sub-0=1, the proposed test statistics are based on the OLS estimator, or its "t"-ratio, of the coefficient on Δ-super-"d"-sub-1"y"-sub-"t" - 1 in a regression of Δ"y-sub-t" on Δ-super-"d"-sub-1"y"-sub-"t" - 1 and, possibly, some lags of Δ"y-sub-t". When "d"-sub-1 is not taken to be known a priori, a pre-estimation of "d"-sub-1 is needed to implement the test. We show that the choice of any "T"-super-1/2-consistent estimator of "d"-sub-1 is an element of [0 ,1) suffices to make the test feasible, while achieving asymptotic normality. Monte-Carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well, both in terms of power and size, when compared with others available in the literature. The paper ends with two empirical applications. Copyright The Econometric Society 2002.

Suggested Citation

  • Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:5:p:1963-2006
    as

    Download full text from publisher

    File URL: http://www.blackwellpublishing.com/ecta/asp/abstract.asp?iid=5&aid=359&vid=70
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

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

    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:ecm:emetrp:v:70:y:2002:i:5:p:1963-2006. 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: http://edirc.repec.org/data/essssea.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.