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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.

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Bibliographic Info

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 10/04.

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Date of creation: Mar 2010
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Handle: RePEc:not:notgts:10/04

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

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References

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  1. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, School of Economics and Management, University of Aarhus.
  2. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1992. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc.
  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. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  5. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(01), pages 243-269, February.
  6. 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).
  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. 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.
  9. 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. Chevillon, Guillaume, 2013. "Robust Cointegration Testing in the Presence of Weak Trends, with an Application to the Human Origin of Global Warming," ESSEC Working Papers WP1320, ESSEC Research Center, ESSEC Business School.
  2. 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 Economía Aplicada, Estudios de Economía Aplicada, vol. 28, pages 519-552, Diciembre.
  3. Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers 32993, University of Mannheim, Department of Economics.

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