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Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break

  • Carsten Trenkler
  • Pentti Saikkonen
  • Helmut Lütkepohl

A test for the cointegrating rank of a vector autoregressive (VAR) process with a possible shift and broken linear trend is proposed. The break point is assumed to be known. The setup is a VAR process for cointegrated variables. The tests are not likelihood ratio tests but the deterministic terms including the broken trends are removed first by a GLS procedure and a likelihood ratio type test is applied to the adjusted series. The asymptotic null distribution of the test is derived and it is shown by a Monte Carlo experiment that the test has better small sample properties in many cases than a corresponding Gaussian likelihood ratio test for the cointegrating rank.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-067.pdf
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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-067.

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Length: 36 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2006-067
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  1. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
  2. Christoffersen, Peter F & Giorgianni, Lorenzo, 2000. "Interest-Rate Arbitrage in Currency Baskets: Forecasting Weights and Measuring Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 242-53, April.
  3. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
  4. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  5. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
  6. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1987. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc.
  7. Saikkonen, Pentti & L tkepohl, Helmut & Trenkler, Carsten, 2006. "Break Date Estimation For Var Processes With Level Shift With An Application To Cointegration Testing," Econometric Theory, Cambridge University Press, vol. 22(01), pages 15-68, February.
  8. A. Scorcu, 2002. "On the Time Stability of the Output-Capital Ratio," Working Papers 434, Dipartimento Scienze Economiche, Universita' di Bologna.
  9. Saikkonen, Pentti & Lutkepohl, Helmut, 2000. "Testing for the Cointegrating Rank of a VAR Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 451-64, October.
  10. Carsten Trenkler, 2008. "Determining p-values for systems cointegration tests with a prior adjustment for deterministic terms," Computational Statistics, Springer, vol. 23(1), pages 19-39, January.
  11. Lütkepohl, Helmut & Saikkonen, Pentti & Trenkler, Carsten, 2001. "Testing for the cointegrating rank of a VAR process with level shift at unknown time," SFB 373 Discussion Papers 2001,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
  13. Attfield, Clifford & Temple, Jonathan, 2004. "Measuring Trend Output: How Useful Are the Great Ratios?," CEPR Discussion Papers 4796, C.E.P.R. Discussion Papers.
  14. Saikkonen, Pentti & Lütkepohl, Helmut, 1997. "Local power of likelihood ratio tests for the cointegrating rank of a VAR process," SFB 373 Discussion Papers 1997,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. Toda, Hiro Y, 1994. "Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks when Linear Trends are Present," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 66-79, February.
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