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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
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    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).

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    File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/07-06.pdf
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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 07/01.

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    Date of creation: Oct 2007
    Date of revision:
    Handle: RePEc:not:notgts:07/01

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    Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
    Phone: (44) 0115 951 5620
    Fax: (0115) 951 4159
    Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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    Related research

    Keywords: Nonlinearity testing; Wald tests; unit root tests; stationarity tests;

    References

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    1. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
    2. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, 03.
    3. Andrew Ang & Geert Bekaert, 1998. "Regime Switches in Interest Rates," NBER Working Papers 6508, National Bureau of Economic Research, Inc.
    4. 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.
    5. n/a, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 164, National Institute of Economic and Social Research.
    6. 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.
    7. Audrino, Francesco, 2006. "Tree-Structured Multiple Regimes in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 338-353, July.
    8. 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.
    9. Barkoulas, John T. & Baum, Christopher F. & Onochie, Joseph, 1997. "A nonparametric investigation of the 90-day t-bill rate," Review of Financial Economics, Elsevier, vol. 6(2), pages 187-198.
    10. 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.
    11. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    12. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    13. 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.
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