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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. Our test is not a likelihood ratio test but the deterministic terms including the broken trends are removed first by a generalized least squares procedure. Then, 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. Moreover, response surface techniques can be used to easily obtain p-values of the test for any possible break date. Copyright 2007 The Authors

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2007.00558.x
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Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 29 (2008)
Issue (Month): 2 (03)
Pages: 331-358

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Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:331-358
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  1. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1991. "Stochastic trends and economic fluctuations," Working Paper Series, Macroeconomic Issues 91-4, Federal Reserve Bank of Chicago.
  2. Saikkonen, Pentti & L tkepohl, Helmut, 1999. "Local Power Of Likelihood Ratio Tests For The Cointegrating Rank Of A Var Process," Econometric Theory, Cambridge University Press, vol. 15(01), pages 50-78, February.
  3. Doornik, Jurgen A, 1998. " Approximations to the Asymptotic Distributions of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-93, December.
  4. 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.
  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. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
  7. Trenkler, Carsten, 2004. "Determining p-values for Systems Cointegration Tests With a Prior Adjustment for Deterministic Terms," Papers 2004,37, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  8. Attfield, Clifford & Temple, Jonathan, 2004. "Measuring Trend Output: How Useful Are the Great Ratios?," CEPR Discussion Papers 4796, C.E.P.R. Discussion Papers.
  9. D'Adda, Carlo & Scorcu, Antonello E., 2003. "On the time stability of the output-capital ratio," Economic Modelling, Elsevier, vol. 20(6), pages 1175-1189, December.
  10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  11. Peter F. Christoffersen & Lorenzo Giorgianni, 1999. "Interest Rate Arbitrage in Currency Baskets; Forecasting Weights and Measuring Risk," IMF Working Papers 99/16, International Monetary Fund.
  12. 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.
  13. 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.
  14. 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.
  15. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, june. pag.
  16. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521839198, june. pag.
  17. 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.
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