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Break Date Estimation For Var Processes With Level Shift With An Application To Cointegration Testing


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  • Saikkonen, Pentti
  • L tkepohl, Helmut
  • Trenkler, Carsten


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 Yrj 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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 01 (February)
Pages: 15-68

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Handle: RePEc:cup:etheor:v:22:y:2006:i:01:p:15-68_06

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Cited by:
  1. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(01), pages 243-269, February.
  2. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2013. "Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion," Econometric Reviews, Taylor & Francis Journals, vol. 32(7), pages 814-847, October.
  3. Karel Mertens, 2006. "How the Removal of Deposit Rate Ceilings Has Changed Monetary Transmission in the US: Theory and Evidence," Economics Working Papers ECO2006/34, European University Institute.
  4. Cortes, Maria, 2007. "Examining Patterns of Bilateral Trade between Australia and Colombia by Using Cointegration Analysis and Error-Correction Models," Economics Working Papers wp07-20, School of Economics, University of Wollongong, NSW, Australia.
  5. Carsten Trenkler & Pentti Saikkonen & Helmut L├╝tkepohl, 2006. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," SFB 649 Discussion Papers SFB649DP2006-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
  7. Maxym Chaban, 2010. "Cointegration analysis with structural breaks and deterministic trends: an application to the Canadian dollar," Applied Economics, Taylor & Francis Journals, vol. 42(23), pages 3023-3037.
  8. Shahbaz, Muhammad & Tahir, Mohammad Iqbal & Ali, Imran & Rehman, Ijaz Ur, 2014. "Is gold investment a hedge against inflation in Pakistan? A co-integration and causality analysis in the presence of structural breaks," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 190-205.


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