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BREAK DATE ESTIMATION FOR VAR PROCESSES WITH LEVEL SHIFT WITH AN APPLICATION TO COINTEGRATION TESTING

Published online by Cambridge University Press:  12 December 2005

Pentti Saikkonen ,
Helmut Lütkepohl  and
Carsten Trenkler
Pentti Saikkonen
Affiliation:
University of Helsinki
Helmut Lütkepohl
Affiliation:
European University Institute, Florence and Humboldt University Berlin
Carsten Trenkler
Affiliation:
Humboldt University Berlin
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Abstract

In testing for the cointegrating rank of a vector autoregressive process it is important to take into account level shifts that have occurred in the sample period. Therefore the properties of estimators of the time period where a shift has taken place are investigated. The possible structural break is modeled as a simple shift in the level of the process. Two alternative estimators for the break date are considered, and their asymptotic properties are derived under various assumptions regarding the size of the shift. In particular, properties of the shift date estimators are obtained under the assumption of an increasing or decreasing size of the shift when the sample size grows. These results are used to explore the implications for testing the cointegrating rank of the process. A previously proposed likelihood ratio type test for the cointegrating rank and a modified version are considered, and their asymptotic properties are derived. It is shown that their asymptotic null distributions are unaffected by the level shift under the assumptions made for the shift size. The performance of the shift date estimators and the cointegrating rank tests in small samples is investigated by simulations.We thank two referees for helpful comments, and we are grateful to the Deutsche Forschungsgemeinschaft, SFB 373, and the European Commission under the Training and Mobility of Researchers Programme (contract ERBFMRXCT980213) for financial support. The first author also acknowledges financial support by the Yrjö Jahnsson Foundation, the Academy of Finland, and the Alexander von Humboldt Foundation under a Humboldt research award. Part of this research was done while he was visiting the Humboldt University in Berlin, and part of the research was carried out while he and the third author were visiting the European University Institute, Florence. An extended version of this paper is available as an EUI discussion paper under the title “Break Date Estimation and Cointegration Testing in VAR Processes with Level Shift,” ECO 2004/21.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 1 , February 2006 , pp. 15 - 68
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Bai, J. (1994) Least squares estimation of a shift in linear processes. Journal of Time Series Analysis 15, 453–472.CrossRefGoogle Scholar
Bai, J., R.L. Lumsdaine, & J.H. Stock (1998) Testing for and dating common breaks in multivariate time series. Review of Economic Studies 65, 395–432.CrossRefGoogle Scholar
Gregory, A.W. & B.E. Hansen (1996) Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126.CrossRefGoogle Scholar
Hubrich, K., H. Lütkepohl, & P. Saikkonen (2001) A review of systems cointegration tests. Econometric Reviews 20, 247–318.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.
Johansen, S., R. Mosconi, & B. Nielsen (2000) Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal 3, 216–249.CrossRefGoogle Scholar
Lütkepohl, H. & P. Saikkonen (2000) Testing for the cointegrating rank of a VAR process with a time trend. Journal of Econometrics 95, 177–198.CrossRefGoogle Scholar
Lütkepohl, H., P. Saikkonen, & C. Trenkler (2004) Testing for the cointegrating rank of a VAR process with level shift at unknown time. Econometrica 72, 647–662.CrossRefGoogle Scholar
Müller, U.K. & G. Elliott (2003) Tests for unit roots and the initial condition. Econometrica 71, 1269–1286.CrossRefGoogle Scholar
Perron, P. (1989) The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361–1401.CrossRefGoogle Scholar
Saikkonen, P. (2001) Consistent estimation in cointegrated vector autoregressive models with nonlinear time trends in cointegrating relations. Econometric Theory 17, 296–326.CrossRefGoogle Scholar
Saikkonen, P. & H. Lütkepohl (2000a) Testing for the cointegrating rank of a VAR process with structural shifts. Journal of Business & Economic Statistics 18, 451–464.Google Scholar
Saikkonen, P. & H. Lütkepohl (2000b) Trend adjustment prior to testing for the cointegrating rank of a vector autoregressive process. Journal of Time Series Analysis 21, 435–456.Google Scholar
Saikkonen, P. & H. Lütkepohl (2002) Testing for a unit root in a time series with a level shift at unknown time. Econometric Theory 18, 313–348.Google Scholar
Saikkonen, P., H. Lütkepohl, & C. Trenkler (2004) Break Date Estimation and Cointegration Testing in VAR Processes with Level Shift. European University Institute, Florence, Discussion paper ECO 2004/21.
Toda, H.Y. (1994) Finite sample properties of likelihood ratio tests for cointegrating ranks when linear trends are present. Review of Economics and Statistics 76, 66–79.CrossRefGoogle Scholar