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

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  • Carsten Trenkler
  • Pentti Saikkonen
  • Helmut Lütkepohl

Abstract

. 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.

Suggested Citation

  • Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2008. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 331-358, March.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:331-358
    DOI: 10.1111/j.1467-9892.2007.00558.x
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    1. 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.
    2. Cliff L.F. Attfield & Jonathan R.W. Temple, 2003. "Measuring trend output: how useful are the Great Ratios?," Bristol Economics Discussion Papers 03/555, School of Economics, University of Bristol, UK.
    3. 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 451-464, October.
    4. 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.
    5. 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 242-253, April.
    6. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    7. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    8. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-840, September.
    9. Saikkonen, Pentti & Lütkepohl, Helmut, 1999. "Local Power Of Likelihood Ratio Tests For The Cointegrating Rank Of A Var Process," Econometric Theory, Cambridge University Press, vol. 15(1), pages 50-78, February.
    10. 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.
    11. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2004. "Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time," Econometrica, Econometric Society, vol. 72(2), pages 647-662, March.
    12. 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.
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    3. Arsova, Antonia & Karaman Örsal, Deniz Dilan, 2021. "A panel cointegrating rank test with structural breaks and cross-sectional dependence," Econometrics and Statistics, Elsevier, vol. 17(C), pages 107-129.
    4. Koukouritakis, Minoas, 2013. "Expectations hypothesis in the context of debt crisis: Evidence from five major EU countries," Research in Economics, Elsevier, vol. 67(3), pages 243-258.
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    7. Martins Iyoboyi & Ummu Ahmad Jalingo & Ahmad Tsauni, 2016. "Impact of Institutions on Macroeconomic Performance in Nigeria: 1980-2013," Eastern European Business and Economics Journal, Eastern European Business and Economics Studies Centre, vol. 2(3), pages 193-221.
    8. Koukouritakis, Minoas & Papadopoulos, Athanasios P. & Yannopoulos, Andreas, 2014. "Transmission effects in the presence of structural breaks: Evidence from South-Eastern European countries," Economic Modelling, Elsevier, vol. 41(C), pages 298-311.
    9. Deniz Dilan Karaman Örsal, 2008. "Comparison of Panel Cointegration Tests," Economics Bulletin, AccessEcon, vol. 3(6), pages 1-20.
    10. Skrobotov, Anton, 2021. "Structural breaks in cointegration models: Multivariate case," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 64, pages 83-106.
    11. 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.
    12. Razvan Pascalau & Junsoo Lee & Saban Nazlioglu & Yan (Olivia) Lu, 2022. "Johansen‐type cointegration tests with a Fourier function," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 828-852, September.
    13. Nikolaos Giannellis & Minoas Koukouritakis, 2016. "Eurozone's Leader and its Followers: Are their Markets Integrated Enough?," Working Papers 1607, University of Crete, Department of Economics.
    14. Giannellis, Nikolaos & Koukouritakis, Minoas, 2017. "Competitiveness divergence in the Eurozone: The need for symmetric adjustment," Journal of Policy Modeling, Elsevier, vol. 39(5), pages 942-962.
    15. Léonore Raguideau-Hannotin, 2021. "Monetary autonomy of CESEE countries and nominal convergence in EMU: a cointegration analysis with structural breaks," EconomiX Working Papers 2021-20, University of Paris Nanterre, EconomiX.
    16. Michał Majsterek & Emilia Gosińska, 2020. "Structural Change in the Deterministic and Stochastic Part of VECM. I(1) and I(2) Case," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(4), pages 317-345, December.
    17. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
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    19. Lindback, Morten & Osmundsen, Petter & Øglend, Atle, 2013. "Shale Gas and the Relationship between U.S. Natural Gas, Liquified Petroleum Gases and Oil Market," UiS Working Papers in Economics and Finance 2013/5, University of Stavanger.
    20. Emilia Gosińska & Aleksander Welfe, 2022. "The Cointegrated VAR Model with Deterministic Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 14(3), pages 335-350, September.

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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