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Testing linear restrictions on cointegration vectors: Sizes and powers of Wald tests in finite samples

  • Haug, Alfred A.

The Wald test for linear restrictions on cointegrating vectors is compared infinite samples using the Monte Carlo method. The Wald test within the vector error-correction based methods of Bewley et al (1994) and of Johansen (1991), the canonical cointegration method of Park (1992) the dynamic ordinary least squares method of Phillips and Loretan (1991), Saikkonen (1991) and Stock and Watson (1993) the fully modified ordinary least squares method of Phillips and Hansen (1990) and the band spectral techniques of Phillips (1991) are considered. In terms of test size Johansen’s method seems to be preferred and in terms of test power it is Park’s and Phillips’. However the relatively poor results in the context of cointegrating regressions suggest that improvements on the performance of the Wald tests considered here are needed.

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Paper provided by Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen in its series Technical Reports with number 1999,04.

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Date of creation: 1999
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Handle: RePEc:zbw:sfb475:199904
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  1. Haug, A.A., 1992. "Tests for Cointegration: A Monte Carlo Comparison," Papers 93-2, York (Canada) - Department of Economics.
  2. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation for Research in Economics, Yale University.
  3. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  4. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  5. Bewley, Ronald & Orden, David & Yang, Minxian & Fisher, Lance A., 1994. "Comparison of Box--Tiao and Johansen canonical estimators of cointegrating vectors in VEC(1) models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 3-27.
  6. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Ho, Mun S & Sorensen, Bent E, 1996. "Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 726-32, November.
  9. Rossana, Robert J & Seater, John J, 1995. "Temporal Aggregation and Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 441-51, October.
  10. Gregory, Allan W, 1994. "Testing for Cointegration in Linear Quadratic Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 347-60, July.
  11. Kitamura, Yuichi & Phillips, Peter C.B., 1995. "Efficient IV Estimation in Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1095-1130, October.
  12. Peter C.B. Phillips & Mico Loretan, 1989. "Estimating Long Run Economic Equilibria," Cowles Foundation Discussion Papers 928, Cowles Foundation for Research in Economics, Yale University.
  13. Yang, Minxian & Bewley, Ronald, 1996. "On cointegration tests for VAR models with drift," Economics Letters, Elsevier, vol. 51(1), pages 45-50, April.
  14. Inder, Brett, 1993. "Estimating long-run relationships in economics : A comparison of different approaches," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 53-68.
  15. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  16. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
  17. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  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(05), pages 1015-1032, October.
  19. Minxian, Yang, 1998. "System estimators of cointegrating matrix in absence of normalising information," Journal of Econometrics, Elsevier, vol. 85(2), pages 317-337, August.
  20. Bossaerts, Peter, 1988. "Common nonstationary components of asset prices," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 347-364.
  21. Bera, A. K. & Byron, R. P. & Jarque, C. M., 1981. "Further evidence on asymptotic tests for homogeneity and symmetry in large demand systems," Economics Letters, Elsevier, vol. 8(2), pages 101-105.
  22. 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.
  23. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
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