IDEAS home Printed from https://ideas.repec.org/p/ins/quaeco/qf04024.html
   My bibliography  Save this paper

The likelihood ratio test for the rank of a cointegration submatrix

Author

Listed:
  • Paruolo Paolo

    (Department of Economics, University of Insubria, Italy)

Abstract

This paper proposes a likelihood ratio test for rank-dficiency of a sub- matrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent-transitory decompositions and of subhypotheses related to neutrality and long run Granger noncausality. The proposed test has x2 limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable.

Suggested Citation

  • Paruolo Paolo, 2004. "The likelihood ratio test for the rank of a cointegration submatrix," Economics and Quantitative Methods qf04024, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf04024
    as

    Download full text from publisher

    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2004_35.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    2. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    3. repec:cup:etheor:v:13:y:1997:i:1:p:79-118 is not listed on IDEAS
    4. Kasa, Kenneth, 1992. "Common stochastic trends in international stock markets," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 95-124, February.
    5. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    6. Paolo Paruolo, 2001. "The Power of Lambda Max," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(3), pages 395-403, July.
    7. Kurozumi, Eiji, 2005. "The Rank Of A Submatrix Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 299-325, April.
    8. Catherine Bruneau & Eric Jondeau, 1999. "Long‐run Causality, with an Application to International Links Between Long‐term Interest Rates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 545-568, November.
    9. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    10. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.
    11. Paruolo, Paolo, 2002. "Asymptotic Inference On The Moving Average Impact Matrix In Cointegrated I (2) Var Systems," Econometric Theory, Cambridge University Press, vol. 18(3), pages 673-690, June.
    12. Taku Yamamoto & Eiji Kurozumi, 2006. "Tests for Long‐Run Granger Non‐Causality in Cointegrated Systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 703-723, September.
    13. repec:bla:obuest:v:61:y:1999:i:4:p:545-68 is not listed on IDEAS
    14. Andrews, Donald W K, 1996. "Admissibility of the Likelihood Ratio Test When the Parameter Space Is Restricted under the Alternative," Econometrica, Econometric Society, vol. 64(3), pages 705-718, May.
    15. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    16. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-399, October.
    17. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    18. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    19. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
    20. Søren Johansen, 2005. "Interpretation of Cointegrating Coefficients in the Cointegrated Vector Autoregressive Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 93-104, February.
    21. Pentti Saikkonen, 1999. "Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 235-257.
    22. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-160, April.
    23. Luukkonen, Ritva & Ripatti, Antti & Saikkonen, Pentti, 1999. "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 195-204, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cubadda, Gianluca, 2007. "A unifying framework for analysing common cyclical features in cointegrated time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 896-906, October.
    2. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
    3. Fanelli, Luca & Paruolo, Paolo, 2010. "Speed of adjustment in cointegrated systems," Journal of Econometrics, Elsevier, vol. 158(1), pages 130-141, September.
    4. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    5. Emerson Fernandes Marçal & Priscila Fernandes Ribeiro, 2011. "Levado pelos Fundamentos? Estimando o Desalinhamento Cambial Norte-Americano a partir de Técnicas de Cointegração," Discussion Papers 1674, Instituto de Pesquisa Econômica Aplicada - IPEA.
    6. Emerson Fernandes Marçal & Fernando Barbi, 2010. "“Quo Vadis Real? Estimating the Brazilian Real Exchange Rate Misalignment in Vector Error Correction Model with Structural Change”," Working Papers 10-2010, Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto.
    7. Bertocco Giancarlo, 2006. "Are banks special? A note on Tobin’s theory of financial intermediaries," Economics and Quantitative Methods qf0605, Department of Economics, University of Insubria.
    8. Kurita, Takamitsu, 2020. "Normalising cointegrating relationships subject to long-run exclusion," Economics Letters, Elsevier, vol. 192(C).

    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. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    2. Norman J. Morin, 2006. "Likelihood ratio tests on cointegrating vectors, disequilibrium adjustment vectors, and their orthogonal complements," Finance and Economics Discussion Series 2006-21, Board of Governors of the Federal Reserve System (U.S.).
    3. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    4. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    5. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    6. Massimo Franchi & Paolo Paruolo, 2019. "A general inversion theorem for cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1176-1201, November.
    7. Christophe RAULT, 2007. "Une synthèse de l'exogénéité dans les modèles Vectoriels à Correction d'Erreurs," LEO Working Papers / DR LEO 1723, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    8. 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.
    9. Masih, Rumi & Masih, Abul M. M., 2001. "Long and short term dynamic causal transmission amongst international stock markets," Journal of International Money and Finance, Elsevier, vol. 20(4), pages 563-587, August.
    10. Emerson Fernandes Marçal & Priscila Fernandes Ribeiro, 2011. "Levado pelos Fundamentos? Estimando o Desalinhamento Cambial Norte-Americano a partir de Técnicas de Cointegração," Discussion Papers 1674, Instituto de Pesquisa Econômica Aplicada - IPEA.
    11. Marçal, Emerson Fernandes & Zimmermann, Beatrice & de Prince, Diogo & Merlin, Giovanni, 2018. "Assessing interdependence among countries' fundamentals and its implications for exchange rate misalignment estimates: An empirical exercise based on GVAR," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 72(4), December.
    12. Bertocco Giancarlo, 2006. "Are banks special? A note on Tobin’s theory of financial intermediaries," Economics and Quantitative Methods qf0605, Department of Economics, University of Insubria.
    13. Fanelli, Luca & Paruolo, Paolo, 2010. "Speed of adjustment in cointegrated systems," Journal of Econometrics, Elsevier, vol. 158(1), pages 130-141, September.
    14. Qizilbash, M., 1995. "Egalitarian justice, capability and well-being prospects," Discussion Paper Series In Economics And Econometrics 9516, Economics Division, School of Social Sciences, University of Southampton.
    15. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    16. Eleni Constantinou & Avo Kazandjian & Georgios P. Kouretas & Vera Tahmazian, 2008. "Common Stochastic Trends Among The Cyprus Stock Exchange And The Ase, Lse And Nyse," Bulletin of Economic Research, Wiley Blackwell, vol. 60(4), pages 327-349, October.
    17. Joseph, Kishore & Garcia, Philip & Peterson, Paul E., 2016. "Does the Boxed Beef Price Inform the Live Cattle Futures Price?," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 236166, Agricultural and Applied Economics Association.
    18. Tom Engsted & Jesper Lund, 1997. "Common stochastic trends in international stock prices and dividends: an example of testing overidentifying restrictions on multiple cointegration vectors," Applied Financial Economics, Taylor & Francis Journals, vol. 7(6), pages 659-665.
    19. Diamandis, Panayiotis F., 2009. "International stock market linkages: Evidence from Latin America," Global Finance Journal, Elsevier, vol. 20(1), pages 13-30.
    20. Pesaran, M. Hashem & Shin, Yongcheol, 1996. "Cointegration and speed of convergence to equilibrium," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 117-143.

    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:ins:quaeco:qf04024. 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: Segreteria Dipartimento (email available below). General contact details of provider: https://edirc.repec.org/data/feinsit.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.