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Testing for nonlinear trends when the order of integration is unknown

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  • David I. Harvey
  • Stephen J. Leybourne
  • Lisa Xiao
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    Abstract

    We consider testing for the presence of nonlinearities in the mean and/or trend of a time series, approximating the potential nonlinear behaviour using a Fourier function expansion. In contrast to procedures that are currently available, we develop tests that are robust to the order of integration, in the sense that they are asymptotically correctly sized regardless of whether the stochastic component of the series is stationary or contains a unit root. The tests we propose take the form of Wald statistics based on cumulated series, together with a correction factor to line up the asymptotic critical values across the I(0) and I(1) environments. The local asymptotic power and finite sample properties of the tests are evaluated using various different correction factors. We envisage that the testing procedure we recommend should be very useful to applied researchers wishing to draw robust inference regarding the presence of nonlinear trend components in a series.

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    File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/09-04.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 09/04.

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    Date of creation: Aug 2009
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    Handle: RePEc:not:notgts:09/04

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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: Trend function testing; Robust tests; Fourier approximation;

    References

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    1. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
    2. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
    3. Harvey David I & Leybourne Stephen J & Taylor A.M. Robert, 2006. "On Robust Trend Function Hypothesis Testing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-27, March.
    4. Ralf Becker & Walter Enders & Junsoo Lee, 2006. "A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 381-409, 05.
    5. 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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