IDEAS home Printed from https://ideas.repec.org/p/hhb/hanken/0499.html
   My bibliography  Save this paper

A General Test for the Cointegrating Rank in Vector Autoregressive Models

Author

Listed:
  • Ahlgren, Niklas

    (Swedish School of Economics and Business Administration)

  • Nyblom, Jukka

    (University of Joensuu)

Abstract

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.

Suggested Citation

  • Ahlgren, Niklas & Nyblom, Jukka, 2003. "A General Test for the Cointegrating Rank in Vector Autoregressive Models," Working Papers 499, Hanken School of Economics.
    • 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.
    as

    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.

    References listed on IDEAS

    as
    1. Saikkonen, Pentti & Lütkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(3), pages 373-406, June.
    2. 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 1057-1072, June.
    3. repec:cup:etheor:v:13:y:1997:i:4:p:529-57 is not listed on IDEAS
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    6. 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 113-144, January.
    7. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(4), pages 529-557, February.
    8. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    9. repec:cup:etheor:v:11:y:1995:i:5:p:1015-32 is not listed on IDEAS
    10. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    12. 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.
    13. Toda, Hiro Y., 1995. "Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1015-1032, October.
    14. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boswijk, H. Peter & Jansson, Michael & Nielsen, Morten Ørregaard, 2015. "Improved likelihood ratio tests for cointegration rank in the VAR model," Journal of Econometrics, Elsevier, vol. 184(1), pages 97-110.
    2. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    3. Shintani, Mototsugu, 2001. "A simple cointegrating rank test without vector autoregression," Journal of Econometrics, Elsevier, vol. 105(2), pages 337-362, December.
    4. Isabel Cortés-Jiménez & Manuel Artís, 2005. "The role of the tourism sector in economic development - Lessons from the Spanish experience," ERSA conference papers ersa05p488, European Regional Science Association.
    5. Breitung, Jörg, 1998. "Canonical correlation statistics for testing the cointegration rank in a reversed order," SFB 373 Discussion Papers 1998,105, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Örsal, Deniz Dilan Karaman, 2007. "Comparison of panel cointegration tests," SFB 649 Discussion Papers 2007-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(1), pages 243-269, February.
    8. Lütkepohl, Helmut, 1999. "Vector autoregressive analysis," SFB 373 Discussion Papers 1999,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    10. Masih, Abul M. M. & Masih, Rumi, 1999. "Are Asian stock market fluctuations due mainly to intra-regional contagion effects? Evidence based on Asian emerging stock markets," Pacific-Basin Finance Journal, Elsevier, vol. 7(3-4), pages 251-282, August.
    11. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
    12. Bo Zhou, 2023. "Semiparametrically Optimal Cointegration Test," Papers 2305.08880, arXiv.org.
    13. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    14. Lütkepohl, Helmut, 1999. "Vector autoregressions," SFB 373 Discussion Papers 1999,4, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Matei Demetrescu & Helmut Lütkepohl & Pentti Saikkonen, 2009. "Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 414-435, November.
    16. Tsung Wu Ho, 1999. "Export-orientation and investment-saving correlation: a case of Taiwan," Applied Economics, Taylor & Francis Journals, vol. 31(7), pages 805-813.
    17. Ahmed, Walid M.A., 2011. "Comovements and Causality of Sector Price Indices: Evidence from the Egyptian Stock Exchange," MPRA Paper 28127, University Library of Munich, Germany.
    18. Zhou, Bo, 2024. "Semiparametrically optimal cointegration test," Journal of Econometrics, Elsevier, vol. 242(2).
    19. Elisa Yamazaki Tanabe & José Carlos Ramírez Sánchez, 2010. "Evaluación del impacto del mercado de derivados en los canales de transmisión de la política monetaria en México: Metodologías VAR y M-GARCH," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 4(2), pages 47-78.
    20. M. T. Alguacil & V. Orts, 2003. "Inward Foreign Direct Investment and Imports in Spain," International Economic Journal, Taylor & Francis Journals, vol. 17(3), pages 19-38.

    More about this item

    Keywords

    Common trends; Companion matrix; Eigenvalue test; Integration of order 2; Rank determination; Unit roots;
    All these keywords.

    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:hhb:hanken:0499. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: Staffan Dellringer (email available below). General contact details of provider: https://edirc.repec.org/data/shhhhfi.html .

    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.