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

Author

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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    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(5), pages 829-864, October.
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