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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.

Suggested Citation

  • Paulo M.M. Rodrigues & A. M. Robert Taylor, 2009. "The Flexible Fourier Form and Local GLS De-trended Unit Root Tests," Working Papers w200919, Banco de Portugal, Economics and Research Department.
    • Handle: RePEc:ptu:wpaper:w200919
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    References listed on IDEAS

    as
    1. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1754-1792, December.
    2. Schmidt, Peter & Lee, Junsoo, 1991. "A modification of the Schmidt-Phillips unit root test," Economics Letters, Elsevier, vol. 36(3), pages 285-289, July.
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    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    5. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    6. 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.
    7. 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.
    8. 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.
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    11. 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.
    12. 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, May.
    13. 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.
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    Cited by:

    1. Christopoulos, Dimitris K. & León-Ledesma, Miguel A., 2010. "Smooth breaks and non-linear mean reversion: Post-Bretton Woods real exchange rates," Journal of International Money and Finance, Elsevier, vol. 29(6), pages 1076-1093, October.
    2. Fumitaka FURUOKA, 2014. "Does Hysteresis Exist in Unemployment? New Findings from Fourteen Regions of the Czech Republic," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 64(1), pages 59-78, February.
    3. Jing-Ping Li & Omid Ranjbar & Tsangyao Chang, 2017. "Unemployment Hysteresis In Piigs Countries: A New Test With Both Sharp And Smooth Breaks," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 62(05), pages 1165-1177, December.
    4. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    5. Nazlioglu, Saban & Gupta, Rangan & Bouri, Elie, 2020. "Movements in international bond markets: The role of oil prices," International Review of Economics & Finance, Elsevier, vol. 68(C), pages 47-58.
    6. Tolga Omay & Muhammad Shahbaz & Chris Stewart, 2021. "Is there really hysteresis in the OECD unemployment rates? New evidence using a Fourier panel unit root test," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 48(4), pages 875-901, November.
    7. Omay, Tolga & Shahbaz, Muhammad & Stewart, Chris, 2021. "Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test," MPRA Paper 107691, University Library of Munich, Germany, revised 10 May 2021.
    8. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Tolga Omay, 2019. "Does U.K.’s Real GDP have a Unit Root? Evidence from a Multi-Century Perspective," Working Papers 201926, University of Pretoria, Department of Economics.

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    More about this item

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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