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Testing for the cointegrating rank of a VAR process with level shift and trend break

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  • Trenkler, Carsten
  • Saikkonen, Pentti
  • Lütkepohl, Helmut

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. 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.

Suggested Citation

  • Trenkler, Carsten & Saikkonen, Pentti & Lütkepohl, Helmut, 2006. "Testing for the cointegrating rank of a VAR process with level shift and trend break," SFB 649 Discussion Papers 2006-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-067
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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 & Lütkepohl, 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(1), pages 15-68, February.
    4. Saikkonen, Pentti & Lütkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(3), pages 373-406, June.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, September.
    12. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    14. 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.
    15. 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.
    16. repec:bla:jecsur:v:12:y:1998:i:5:p:573-93 is not listed on IDEAS
    17. 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.
    18. 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.
    19. 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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    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.
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    11. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
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    14. Giannellis, Nikolaos & Koukouritakis, Minoas, 2013. "Exchange rate misalignment and inflation rate persistence: Evidence from Latin American countries," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 202-218.
    15. 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.
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    More about this item

    Keywords

    Cointegration; structural break; vector autoregressive process; error correction model;
    All these keywords.

    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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