Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T17:25:37.827Z Has data issue: false hasContentIssue false
  • English
  • Français

TESTING THE NULL OF NO COINTEGRATION WHEN COVARIATES ARE KNOWN TO HAVE A UNIT ROOT

Published online by Cambridge University Press:  01 December 2009

Graham Elliott and
Elena Pesavento
Graham Elliott
Affiliation:
University of California, San Diego
Elena Pesavento*
Affiliation:
Emory University
*
*Address correspondence to Elena Pesavento, Emory University, 1602 Fishburne Dr., Atlanta, GA 30322; e-mail: epesave@emory.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A number of tests have been suggested for the test of the null of no cointegration. Under this null, correlations are spurious in the sense of Granger and Newbold (1974) and Phillips (1986). We examine a set of models local to the null of no cointegration and derive tests with optimality properties in order to examine the efficiency of available tests. We find that, for a sufficiently tight weighting over potential cointegrating vectors, commonly employed full system tests have power that can, in some situations, be quite far from the power bounds for the models examined.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009, pp. 1829 - 1850
Copyright
Copyright © Cambridge University Press 2009

References

REFERENCES

Andrews, D. & Ploberger, W. (1994) Optimal tests when the nuisance parameter is only present under the alternative. Econometrica 62, 1383–1414.CrossRefGoogle Scholar
Banerjee, A., Dolado, J.J., Hendry, D.F., & Smith, G.W. (1986) Exploring equilibrium relationship in econometrics through static models: Some Monte Carlo evidence. Oxford Bulletin of Economics and Statistics 48, 253–277.CrossRefGoogle Scholar
Boswijk, H.P. (1994) Testing for an unstable root in conditional and structural error correction models. Journal of Econometrics 63, 37–60.CrossRefGoogle Scholar
Davies, R.B. (1977) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247–254.CrossRefGoogle Scholar
Davies, R.B. (1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33–43.Google Scholar
Elliott, G. & Jansson, M. (2003) Testing for unit roots with stationary covariates. Journal of Econometrics 115, 75–89.CrossRefGoogle Scholar
Elliott, G., Jansson, M., & Pesavento, E. (2005) Optimal power for testing potential cointegrating vectors with known parameters for nonstationarity. Journal of Business & Economic Statistics 23:1, 34–48.CrossRefGoogle Scholar
Elliott, G., Rothenberg, T.J., & Stock, J. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W. (1987) Cointegration and error correction: representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Granger, C.W. & Newbold, P. (1974) Spurious regressions in econometrics. Journal of Econometrics 2, 111–120.CrossRefGoogle Scholar
Hansen, B.E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64(1), 413–430.CrossRefGoogle Scholar
Jansson, M. (2007) Semiparmetric Power Envelopes for Tests of the Unit Root Hypothesis. Mimeo, UC Berkeley.CrossRefGoogle Scholar
Johansen, S. (1988) Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231–254.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood Based Inference in Cointegrated Autoregressive Models. Oxford University Press.CrossRefGoogle Scholar
Johansen, S. & Juselius, K. (1990) Maximum likelihood estimation and inference on cointegration with application to the demand for money. Oxford Bulletin of Economics and Statistics 52, 169–210.CrossRefGoogle Scholar
King, M. (1988) Towards a theory of point optimal testing. Econometric Reviews 6, 169–218.CrossRefGoogle Scholar
Kremers, J.M., Ericsson, N.R., & Dolado, J.J. (1992) The power of cointegration tests. Oxford Bulletin of Economics and Statistics 54, 325–348.CrossRefGoogle Scholar
Mueller, U.K. (2007) An Alternative Sense of Asymptotic Efficiency. Mimeo, Princeton University.Google Scholar
Mueller, U.K. & Elliott, G. (2003) Tests for unit roots and the initial observation. Econometrica 71, 1269–1286.CrossRefGoogle Scholar
Pesavento, E. (2004) An analytical evaluation of the power of tests for the absence of cointegration. Journal of Econometrics 122(2), 349–384.CrossRefGoogle Scholar
Pesavento, E. (2007) Residuals based tests for the null of no cointegration: An analytical comparison. Journal of Time Series Analysis 28(1), 111–137.CrossRefGoogle Scholar
Phillips, P.C.B. (1986) Understanding spurious regressions in econometrics. Journal of Econometrics 33(3), 311–340.CrossRefGoogle Scholar
Phillips, P.C.B. & Ouliaris, S. (1990) Asymptotic properties of residuals based tests for cointegration. Econometrica 58, 165–193.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics of linear processes. Annals Of Statistics 20, 971–1001.CrossRefGoogle Scholar
Rothenberg, T.J. & Stock, J.H. (1993) Inference in a nearly integrated model with nonnormal innovations. Journal of Econometrics 80, 269–286.CrossRefGoogle Scholar
Zivot, E. (2000) The power of single equation tests for cointegration when the cointegrating vector is prespecified. Econometric Theory 16, 407–439.CrossRefGoogle Scholar