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Bootstrap co-integration rank testing: the role of deterministic variables and initial values in the bootstrap recursion

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  • Giuseppe Cavaliere
  • A. M. Robert Taylor
  • Carsten Trenkler

Abstract

In this paper we investigate the role of deterministic components and initial values in bootstrap likelihood ratio type tests of co-integration rank. A number of bootstrap procedures have been proposed in the recent literature some of which include estimated deterministic components and non-zero initial values in the bootstrap recursion while others do the opposite. To date, however, there has not been a study into the relative performance of these two alternative approaches. In this paper we fill this gap in the literature and consider the impact of these choices on both OLS and GLS de-trended tests, in the case of the latter proposing a new bootstrap algorithm as part of our analysis. Overall, for OLS de-trended tests our findings suggest that it is preferable to take the computationally simpler approach of not including estimated deterministic components in the bootstrap recursion and setting the initial values of the bootstrap recursion to zero. For GLS de-trended tests, we find that the approach of Trenkler (2009), who includes a restricted estimate of the deterministic component in the bootstrap recursion, can improve finite sample behaviour further.

Suggested Citation

  • Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2010. "Bootstrap co-integration rank testing: the role of deterministic variables and initial values in the bootstrap recursion," Discussion Papers 10/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:10/04
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    References listed on IDEAS

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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. 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.
    3. 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.
    4. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(1), pages 243-269, February.
    5. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    6. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    7. 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.
    8. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    9. 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.
    10. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
    11. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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    Cited by:

    1. Hutter, Christian & Klinger, Sabine & Trenkler, Carsten & Weber, Enzo, 2019. "Which factors are behind Germany's labour market upswing?," IAB-Discussion Paper 201920, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    2. Guillaume Chevillon, 2017. "Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 514-545, May.
    3. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 272-289, May.
    4. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2015. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(5), pages 740-759, October.
    5. repec:hal:journl:hal-00914830 is not listed on IDEAS
    6. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, Robert, 2010. "Determination of the Number of Common Stochastic Trends Under Conditional Heteroskedasticity/Determinación del número de tendencias estocásticas comunes bajo heteroscedasticidad condicional," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 519-552, Diciembre.

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    Keywords

    Co-integration; trace tests; i.i.d. bootstrap; OLS and GLS de-trending;
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