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Behavior of the standard Dickey–Fuller test when there is a Fourier-form break under the null hypothesis

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  • Yang, Lixiong
  • Lee, Chingnun
  • Su, Jen-Je

Abstract

We derive the null asymptotic distribution of the standard Dickey–Fuller test with the existence of an unnoticed Fourier component. The so-called converse Perron phenomenon might occur, but only in the trend-case with a low-frequency Fourier component and small error variance.

Suggested Citation

  • Yang, Lixiong & Lee, Chingnun & Su, Jen-Je, 2017. "Behavior of the standard Dickey–Fuller test when there is a Fourier-form break under the null hypothesis," Economics Letters, Elsevier, vol. 159(C), pages 128-133.
    • Handle: RePEc:eee:ecolet:v:159:y:2017:i:c:p:128-133
    DOI: 10.1016/j.econlet.2017.07.016
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    References listed on IDEAS

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    1. Enders, Walter & Lee, Junsoo, 2012. "The flexible Fourier form and Dickey–Fuller type unit root tests," Economics Letters, Elsevier, vol. 117(1), pages 196-199.
    2. Chingnun Lee & Jyh-Lin Wu & Lixiong Yang, 2016. "A Simple Panel Unit-Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 365-393, June.
    3. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    4. Stephen J. Leybourne And Paul Newbold, 2000. "Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 1-15.
    5. 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.
    6. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    7. Walter Enders & Junsoo Lee, 2012. "A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(4), pages 574-599, August.
    8. Leybourne, Stephen J. & C. Mills, Terence & Newbold, Paul, 1998. "Spurious rejections by Dickey-Fuller tests in the presence of a break under the null," Journal of Econometrics, Elsevier, vol. 87(1), pages 191-203, August.
    9. Leybourne, Stephen J. & Newbold, Paul, 2000. "BEHAVIOR OF DICKEY–FULLER t-TESTS WHEN THERE IS A BREAK UNDER THE ALTERNATIVE HYPOTHESIS," Econometric Theory, Cambridge University Press, vol. 16(5), pages 779-789, October.
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    Cited by:

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    2. 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.
    3. Tolga Omay & Perihan Iren, 2023. "Controlling Heterogeneous Structure of Smooth Breaks in Panel Unit Root and Cointegration Testing," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 233-265, January.

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    More about this item

    Keywords

    Structural break; Fourier approximation; Unit root test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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