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A powerful test for linearity when the order of integration is unknown [Revised to become No. 07/06 above]

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  • David I. Harvey
  • Stephen J. Leybourne
  • Bin Xiao

Abstract

In this paper we propose a test of the null hypothesis of time series linearity against a nonlinear alternative, when uncertainty exists as to whether or not the series contains a unit root. We provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against nonlinearity of either form, being asymptotically equivalent to the efficient test in each case. Finite sample simulations show that the new procedure has good size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne & Bin Xiao, 2007. "A powerful test for linearity when the order of integration is unknown [Revised to become No. 07/06 above]," Discussion Papers 07/01, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:07/01
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    File URL: http://www.nottingham.ac.uk/research/groups/grangercentre/documents/07-01.pdf
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    References listed on IDEAS

    as
    1. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2003. "Some Limit Theory For Autocovariances Whose Order Depends On Sample Size," Econometric Theory, Cambridge University Press, vol. 19(05), pages 829-864, October.
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    3. Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.
    4. Harris, David & Leybourne, Stephen & McCabe, Brendan, 2005. "Panel Stationarity Tests for Purchasing Power Parity With Cross-Sectional Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 395-409, October.
    5. Dirk Te Velde, 2001. "Balance of payments prospects in EMU," National Institute of Economic and Social Research (NIESR) Discussion Papers 178, National Institute of Economic and Social Research.
    6. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    7. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
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    9. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, March.
    10. Audrino, Francesco, 2006. "Tree-Structured Multiple Regimes in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 338-353, July.
    11. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    12. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
    13. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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