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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.

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Paper provided by Departamento de Economía - Pontificia Universidad Católica del Perú in its series Documentos de Trabajo / Working Papers with number 2012-327.

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Length: 77 pages
Date of creation: 2012
Date of revision:
Publication status: published
Handle: RePEc:pcp:pucwps:wp00327
Contact details of provider: Postal: Av. Universitaria 1801, San Miguel, Lima, Perú
Phone: (511) 626-2000 ext. 4950, 4951
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Web page: http://departamento.pucp.edu.pe/economia/
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  1. Pesavento, Elena, 2000. "Analytical Evaluation of the Power of Tests for the Absence of Cointegration," University of California at San Diego, Economics Working Paper Series qt4cq4773c, Department of Economics, UC San Diego.
  2. Zivot, Eric, 2000. "The Power Of Single Equation Tests For Cointegration When The Cointegrating Vector Is Prespecified," Econometric Theory, Cambridge University Press, vol. 16(03), pages 407-439, June.
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  8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  9. 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.
  10. 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.
  11. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July.
  12. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
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