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Determining the number of cointegrating relations under rank constraints

Author

Listed:
  • Cavaliere Giuseppe

    (Department of Statistical Science, University of Bologna, Italy)

  • Fanelli Luca

    () (Department of Statistical Sciences, University of Bologna, Italy)

  • Paruolo Paolo

    () (Department of Economics, University of Insubria, Italy)

Abstract

This paper proposes likelihood-based procedures for determining the number of cointegrating vectors in the presence of constraints on the cointegration rank. The tests can be applied when a priori information suggests a lower bound on the number of common stochastic trends in the system. The likelihood ratio trace and and lambda max tests are obtained as special cases of the present setup. The tests are easy to implement and have comparable asymptotic power with respect to the trace test; it is also shown that the constrained tests are more powerful for some local alternatives.

Suggested Citation

  • Cavaliere Giuseppe & Fanelli Luca & Paruolo Paolo, 2001. "Determining the number of cointegrating relations under rank constraints," Economics and Quantitative Methods qf0109, Department of Economics, University of Insubria.
  • Handle: RePEc:ins:quaeco:qf0109
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    File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2001_17.pdf
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    References listed on IDEAS

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    1. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
    2. repec:cup:etheor:v:11:y:1995:i:5:p:984-1014 is not listed on IDEAS
    3. Johansen, Soren, 1992. "Determination of Cointegration Rank in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 383-397, August.
    4. Paruolo, Paolo, 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.
    5. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    6. Dominguez, Emilio & Novales, Alfonso, 2000. "Testing the expectations hypothesis in Eurodeposits," Journal of International Money and Finance, Elsevier, vol. 19(5), pages 713-736, October.
    7. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-840, September.
    8. Mougoue, Mbodja, 1992. "The Term Structure of Interest Rates as a Cointegrated System: Empirical Evidence from the Eurocurrency Market," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 15(3), pages 285-296, Fall.
    9. repec:spr:stmapp:v:10:y:2001:i:1:d:10.1007_bf02511644 is not listed on IDEAS
    10. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-472, August.
    11. 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.
    12. Paolo Paruolo, 2001. "LR cointegration tests when some cointegrating relations are known," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 123-137, January.
    13. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(05), pages 984-1014, October.
    14. Paolo Paruolo, 2002. "On Monte Carlo estimation of relative power," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 65-75, June.
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    Cited by:

    1. Hans Christian Kongsted & Heino Bohn Nielsen, 2004. "Analysing I(2) Systems by Transformed Vector Autoregressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 379-397, July.

    More about this item

    Keywords

    Cointegration rank; Likelihood ratio; Trace test; Asymptotic power;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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