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Cointegration Testing Using Pseudolikelihood Ratio Tests

Published online by Cambridge University Press:  11 February 2009

André Lucas
André Lucas
Affiliation:
Free University Amsterdam
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Abstract

This paper considers pseudomaximum likelihood estimators for vector autoregressive models. These estimators are used to determine the cointegration rank of a multivariate time series process using pseudolikelihood ratio tests. The asymptotic distributions of these tests depend on nuisance parameters if the pseudolikelihood is non-Gaussian. This even holds if the likelihood is correctly specified. The nuisance parameters have a natural interpretation and can be consistently estimated. Some simulation results illustrate the usefulness of the tests: non-Gaussian pseudolikelihood ratio tests generally have a higher power than the Gaussian test of Johansen if the innovations demonstrate leptokurtic behavior.

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Articles
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Econometric Theory , Volume 13 , Issue 2 , April 1997 , pp. 149 - 169
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Copyright © Cambridge University Press 1997

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References

REFERENCES

Bierens, H.J. (1994) Nonparametric Cointegration Analysis. Working paper, Southern Methodist University, Dallas, Texas.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.Google Scholar
Boswijk, P. (1992) Cointegration, Identification and Exogeneity. Inference in Structural Error Correction Models. Ph.D. Thesis, Tinbergen Institute, Amsterdam. Amsterdam: Thesis Publishers.Google Scholar
Cox, D.D. & Llatas, I. (1991) Maximum likelihood type estimation for nearly nonstationary autoregressive time series. Annals of Statistics 19, 1109–1128.CrossRefGoogle Scholar
de Vries, C.G. (1994) Stylized facts of nominal exchange rate returns. In van der Ploeg, F. (ed.), The Handbook of International Macroeconomics, pp. 348–389. Oxford: Blackwell.Google Scholar
Engle, R.F. & Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Franses, P.H. & Lucas, A. (1995) Outlier Robust Cointegration Analysis. Econometric Institute report 9529/A, Erasmus University, Rotterdam.Google Scholar
Gallant, A.R. (1987) Nonlinear Statistical Models. New York: Wiley.CrossRefGoogle Scholar
Gouriéroux, C., Monfort, A., & Trognon, A. (1984) Pseudo maximum likelihood methods: Theory. Econometrica 52, 681–700.CrossRefGoogle Scholar
Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., & Stahel, W.A. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.Google Scholar
Hansen, B.E. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.Google Scholar
Herce, M.A. (1994) Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors. Mimeo, University of North Carolina at Chapel Hill.Google Scholar
Hoek, H., Lucas, A., & van Dijk, H.K. (1995) Classical and Bayesian aspects of robust unit root inference. Journal of Econometrics 69, 27–59.CrossRefGoogle Scholar
Huber, P.J. (1981) Robust Statistics. New York: Wiley.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.CrossRefGoogle Scholar
Johansen, S. (1989) The power function of the likelihood ratio test for cointegration. Lecture Notes in Economics and Mathematical Systems, Econometric Decision Models 366, 323–335.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.Google Scholar
Johansen, S. (1994) The role of the constant and linear terms in cointegration analysis of nonstationary variables. Econometric Reviews 13, 205–229.Google Scholar
Kleibergen, F.R. & van Dijk, H.K. (1994) Direct cointegration testing in error correction models. Journal of Econometrics 63, 61–103.Google Scholar
Knight, K. (1989) Limit theory for autoregressive parameters in an infinite variance random walk. Canadian Journal of Statistics 17, 261–278.CrossRefGoogle Scholar
Lucas, A. (1995a) An outlier robust unit root test with an application to the extended Nelson-Plosser data. Journal of Econometrics 66, 153–174.CrossRefGoogle Scholar
Lucas, A. (1995b) Unit root tests based on M estimators. Econometric Theory 11, 331–346.CrossRefGoogle Scholar
Lucas, A. (1996) Outlier Robust Unit Root Analysis. Ph.D. Thesis, Tinbergen Institute, Amsterdam. Amsterdam: Thesis Publishers.Google Scholar
Manski, C.F. (1984) Adaptive estimation of non-linear regression models. Econometric Reviews 3, 145–194.CrossRefGoogle Scholar
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part I. Econometric Theory 4, 468–497.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.CrossRefGoogle Scholar
Phillips, P.C.B. (1988) Regression theory for near-integrated time series. Econometrica 56, 1021–1043.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59, 283–306.Google Scholar
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–495.Google Scholar
Prucha, I.R. & Kelejian, H.H. (1984) The structure of simultaneous equation estimators: A generalization towards nonnormal disturbances. Econometrica 52, 721–736.CrossRefGoogle Scholar
Rahbek, A.C. (1994) The Power of Some Multivariate Cointegration Tests. Working paper 6, University of Copenhagen.Google Scholar
Stock, J.H. (1994) Unit Roots and Trend Breaks. Mimeo, Harvard University, Cambridge, Massachusetts.Google Scholar
White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica 50, 1–25.Google Scholar