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The Flexible Fourier Form and Local GLS De-trended Unit Root Tests

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  • Paulo M.M. Rodrigues
  • A. M. Robert Taylor

Abstract

In two recent papers Enders and Lee (2008) and Becker et al. (2006) provide Lagrange multiplier and OLS de-trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this paper, we generalise the unit root testing procedure based on local GLS de-trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that although the resulting unit root tests possess good finite sample size and power properties, their limit null distributions are undefined.

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Bibliographic Info

Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200919.

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Date of creation: 2009
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Handle: RePEc:ptu:wpaper:w200919

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  1. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  2. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  3. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. 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.
  5. Schmidt, Peter & Lee, Junsoo, 1991. "A modification of the Schmidt-Phillips unit root test," Economics Letters, Elsevier, vol. 36(3), pages 285-289, July.
  6. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  7. Bierens,Herman J., 1996. "Topics in Advanced Econometrics," Cambridge Books, Cambridge University Press, number 9780521565110, April.
  8. Josep Lluís Carrion-i-Silvestre & Dukpa Kim & Pierre Perron, 2007. "GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses," Boston University - Department of Economics - Working Papers Series wp2008-019, Boston University - Department of Economics.
  9. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
  10. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  11. 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.
  12. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  13. Ralf Becker & Walter Enders & A. Stan Hurn, 2001. "Testing for Time Dependence in Parameters," Research Paper Series 58, Quantitative Finance Research Centre, University of Technology, Sydney.
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Cited by:
  1. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.

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