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Residual test for cointegration with GLS detrended data


  • Pierre Perron

    (Boston University)

  • Gabriel Rodriguez

    (Departamento de Economía - Pontificia Universidad Católica del Perú)


We analyze di¤erent residual-based tests for the null of no cointegration using GLS detrended data. We nd and simulate the limiting distributions of these statistics when GLS demeaned and GLS detrended data are used. The distributions depend of the number of right-hand side variables, the type of deterministic components used in the cointegration equation, and a nuisance parameter R2 which measures the long-run correlation between xt and yt. We present an extensive number of Figures which show the asymptotic power functions of the di¤erent statistics analyzed in this paper. The results show that GLS allows to obtain more asymptotic power in comparison with OLS detrending. The more simple residual-based tests (as the ADF) shows power gains for small values of R2 and for only one right-hand side variable. This evidence is valid for R2 less than 0.4. Figures shows that when R2 is larger, the ECR statistics are better for any value of the right-hand side variables. In particular, evidence shows that the ECR statistic which assumes a known cointegration vector is the most powerful. A set of simulated asymptotic critical values are also presented. Unlike other references, in the present framework we use di¤erent c for di¤erent number of right-hand side variables (xt variables) and according to the set of deterministic components. In this selection, we use a R2 = 0:4, which appears to be a sensible choice.

Suggested Citation

  • Pierre Perron & Gabriel Rodriguez, 2012. "Residual test for cointegration with GLS detrended data," Documentos de Trabajo / Working Papers 2012-327, Departamento de Economía - Pontificia Universidad Católica del Perú.
  • Handle: RePEc:pcp:pucwps:wp00327

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    References listed on IDEAS

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    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.
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    7. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
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    More about this item


    Cointegration; Residual-Based Unit Root Test; ECR Test; OLS and GLS Detrented Data; Hypothesis Testing;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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