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A Powerful Test for Linearity When the Order of Integration is Unknown

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Listed:
  • Harvey David I

    (University of Nottingham)

  • Leybourne Stephen J

    (University of Nottingham)

  • Xiao Bin

    (University of Nottingham)

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 better size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

Suggested Citation

  • Harvey David I & Leybourne Stephen J & Xiao Bin, 2008. "A Powerful Test for Linearity When the Order of Integration is Unknown," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-24, September.
    • Handle: RePEc:bpj:sndecm:v:12:y:2008:i:3:n:2
    DOI: 10.2202/1558-3708.1582
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    References listed on IDEAS

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    1. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, March.
    2. 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.
    3. 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.
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    5. George Kapetanios & Yongcheol Shin & Andy Snell, 2000. "Testing for a Unit Root against Nonlinear STAR Models," Edinburgh School of Economics Discussion Paper Series 69, Edinburgh School of Economics, University of Edinburgh.
    6. Audrino, Francesco, 2006. "Tree-Structured Multiple Regimes in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 338-353, July.
    7. 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.
    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(5), pages 829-864, October.
    9. 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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    13. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 1302-1330, December.
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