IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

A General Test for the Cointegrating Rank in Vector Autoregressive Models

  • Ahlgren, Niklas

    ()

    (Swedish School of Economics and Business Administration)

  • Nyblom, Jukka

    ()

    (University of Joensuu)

Registered author(s):

    The article proposes a general test for the cointegrating rank in vector autoregressive models. The test is based on the eigenvalues of the companion matrix, more precisely on the sum of the real parts of those closest to one. The roots of the companion matrix are often inspected as a diagnostic tool. Here this practice is elevated to the level of a formal test. The asymptotic distribution of the test statistic is derived and tabulated by simulation. The new test is compared with the likelihood ratio test. Neither one of the tests is dominating the other over the entire parameter space. The new test safeguards the researcher against making spurious inferences on the cointegrating rank in the presence of explosive roots and of integration of higher order than one. A numerical illustration is given. It is shown that the limiting distribution of the eigenvalues closest to one of the companion matrix is free of nuisance parameters, a useful result in its own right. When applied to a univariate autoregressive model, the augmented Dickey—Fuller test is obtained. The new test can be regarded as the multivariate version of the Dickey—Fuller coefficent test of a unit root. When there is a single common trend, the suggested test statistic has the same asymptotic distribution as the least squares estimate of the autoregressive coeficent in a univariate first order autoregressive model with a unit root. In the numerical application the test is applied to Swedish money demand data, and it is shown how to determine the cointegrating rank using the new test. The results from a small sample simulation experiment mimicking the actual data used in the application are also discussed.

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below under "Related research" 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.

    Paper provided by Hanken School of Economics in its series Working Papers with number 499.

    as
    in new window

    Length: 37 pages
    Date of creation: 31 Dec 2003
    Date of revision:
    Handle: RePEc:hhb:hanken:0499
    Note: This paper is published as: Ahlgren, Niklas and Nyblom, Jukka (2008), 'Tests against Stationary and Explosive Alternatives in Vector Autoregressive Models', Journal of Time Series Analysis, 29, 421-443.
    Contact details of provider: Postal: Hanken School of Economics, Arkadiankatu 22, P.O.B. 479; FIN 00101 Helsinki, Finland
    Phone: +358-9-431 331
    Fax: +358-9-431 33 333
    Web page: http://www.hanken.fi

    More information through EDIRC

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Toda, Hiro Y., 1995. "Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1015-1032, October.
    2. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
    3. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
    4. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    5. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    6. repec:cup:etheor:v:13:y:1997:i:4:p:529-57 is not listed on IDEAS
    7. Harris, D., 1996. "Principal Components Analysis of Cointegrated Time Series," Monash Econometrics and Business Statistics Working Papers 2/96, Monash University, Department of Econometrics and Business Statistics.
    8. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    9. Saikkonen, Pentti & Lütkepohl, Helmut, 1998. "Testing for the cointegrating rank of a VAR process with an intercept," SFB 373 Discussion Papers 1998,51, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
    11. repec:cup:etheor:v:11:y:1995:i:5:p:1015-32 is not listed on IDEAS
    12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:hhb:hanken:0499. 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: (Staffan Dellringer)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.