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Regression-based analysis of cointegration systems

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  • Javier Gómez Biscarri
  • Javier Hualde

Abstract

Two estimation procedures dominate the cointegration literature: Johansen's maximum likelihood inference on vector autoregressive error correction models, and estimation of Phillips' triangular forms. This latter methodology is essentially semiparametric, focusing on estimating long run parameters by means of cointegrating regressions, but it is less used in practice than Johansen's approach, since its implementation requires prior knowledge of features such as the cointegrating rank and an appropriate set of non-cointegrated regressors. In this paper we develop a simple and automatic procedure (based on unit root and regression-based cointegration testing) which provides an estimator of the cointegrating rank and data-based just-identifying conditions for the cointegrating parameters (leading to a Phillips' triangular form). A Monte Carlo experiment and an empirical example are also provided.

Suggested Citation

  • Javier Gómez Biscarri & Javier Hualde, 2014. "Regression-based analysis of cointegration systems," Working Papers 780, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:780
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    References listed on IDEAS

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    1. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-20.
    2. Paolo Paruolo, 2006. "The Likelihood Ratio Test for the Rank of a Cointegration Submatrix," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 921-948, December.
    3. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(4), pages 529-557, February.
    4. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(2), pages 176-199, April.
    5. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    6. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    8. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    9. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
    10. Kurozumi, Eiji, 2005. "The Rank Of A Submatrix Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 299-325, April.
    11. Choi, In & Ahn, Byung Chul, 1995. "Testing for Cointegration in a System of Equations," Econometric Theory, Cambridge University Press, vol. 11(5), pages 952-983, October.
    12. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    13. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    14. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
    15. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(1), pages 19-35, January.
    16. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    17. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    18. 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.
    19. 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.
    20. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    21. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    22. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    23. 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.
    24. Kevin D. Hoover & Soren Johansen & Katarina Juselius, 2008. "Allowing the Data to Speak Freely: The Macroeconometrics of the Cointegrated Vector Autoregression," American Economic Review, American Economic Association, vol. 98(2), pages 251-255, May.
    25. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    26. 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.
    27. 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.
    28. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
    29. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-160, April.
    30. 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.
    31. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
    32. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-126, February.
    33. Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(4), pages 433-444, December.
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    2. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "A residual-based ADF test for stationary cointegration in I(2) settings," Journal of Econometrics, Elsevier, vol. 184(2), pages 280-294.

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    More about this item

    Keywords

    cointegrating space; Phillips' triangular form; Johansen's methodology; regression-based cointegration testing;
    All these keywords.

    JEL classification:

    • 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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