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Some Finite Sample Results On Testing For Granger Noncausality

We compare testing strategies for Granger noncausality in vector autoregressions (VARs)that may or may not have unit roots and cointegration. Sequential testing methods are examined; these test for cointegration and use either a differenced VAR or a vector error correction model(VECM), in which to undertake the main noncausality test. Basically, these strategies attempt to verify the validity of appropriate standard limit theory. We contrast such methods with an augmented lag approach that ensures the limiting Chi Square null distribution irrespective of the data’s nonstationarity characteristics. Our simulations involve bivariate and trivariate VARs in which we allow for the lag order to be selected by general to specific testing as well as by model selection criteria. We find that the current practice of pretesting for cointegration can result in severe over-rejections of the noncausal null while overfitting results in better control of the Type I error probability with often little loss in power.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0305.

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Length: 35 pages
Date of creation: 30 May 2003
Date of revision:
Handle: RePEc:vic:vicewp:0305
Note: ISSN 1485-6441
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  1. Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-28, August.
  2. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-77, Sept.-Oct.
  3. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  4. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality: A Theoretical Overview and Simulation Study," Cowles Foundation Discussion Papers 1001, Cowles Foundation for Research in Economics, Yale University.
  5. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
  6. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  7. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  9. Hoffman, Dennis L & Rasche, Robert H, 1996. "Assessing Forecast Performance in a Cointegrated System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 495-517, Sept.-Oct.
  10. Boudjellaba, Hafida & Dufour, Jean-Marie & Roy, Roch, 1994. "Simplified conditions for noncausality between vectors in multivariate ARMA models," Journal of Econometrics, Elsevier, vol. 63(1), pages 271-287, July.
  11. 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.
  12. Dolado, J.J. & Lutkepohl, H., 1994. "Making Wald Tests Work for Cointegrated Var Systems," Papers 9424, Centro de Estudios Monetarios Y Financieros-.
  13. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
  14. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  15. Yamada, Hiroshi & Toda, Hiro Y., 1998. "Inference in possibly integrated vector autoregressive models: some finite sample evidence," Journal of Econometrics, Elsevier, vol. 86(1), pages 55-95, June.
  16. Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "Specification via model selection in vector error correction models," Economics Letters, Elsevier, vol. 60(3), pages 321-328, September.
  17. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  18. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  19. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-70, October.
  20. Nishii, R., 1988. "Maximum likelihood principle and model selection when the true model is unspecified," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 392-403, November.
  21. Mosconi, Rocco & Giannini, Carlo, 1992. "Non-causality in Cointegrated Systems: Representation Estimation and Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 399-417, August.
  22. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  23. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  24. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  25. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality," Cowles Foundation Discussion Papers 977, Cowles Foundation for Research in Economics, Yale University.
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