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Smooth Break Detection and De-Trending in Unit Root Testing

Author

Listed:
  • Furkan Emirmahmutoglu

    (Department of Econometrics, Ankara Haci Bayram Veli University, 06500 Ankara, Turkey)

  • Tolga Omay

    (Department of Economics, Atilim University, 06830 Ankara, Turkey
    Montpellier Business School, University of Montpellier, Montpellier Research in Management, 34080 Montpellier, France)

  • Syed Jawad Hussain Shahzad

    (Montpellier Business School, University of Montpellier, Montpellier Research in Management, 34080 Montpellier, France
    Department of Accounting, Analysis and Audit, South Ural State University, 454080 Chelyabinsk, Russia)

  • Safwan Mohd Nor

    (Faculty of Business, Economics and Social Development, University of Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
    Victoria Institute of Strategic Economic Studies, Victoria University, Melbourne, VIC 3000, Australia)

Abstract

This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks.

Suggested Citation

  • Furkan Emirmahmutoglu & Tolga Omay & Syed Jawad Hussain Shahzad & Safwan Mohd Nor, 2021. "Smooth Break Detection and De-Trending in Unit Root Testing," Mathematics, MDPI, vol. 9(4), pages 1-25, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:371-:d:498649
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    References listed on IDEAS

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    5. 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.
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    8. Furkan Emirmahmutoglu & Rangan Gupta & Stephen M. Miller & Tolga Omay, 2020. "Is real per capita state personal income stationary? New nonlinear, asymmetric panel‐data evidence," Bulletin of Economic Research, Wiley Blackwell, vol. 72(1), pages 50-62, January.
    9. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Tolga Omay, 2020. "Does real U.K. GDP have a unit root? Evidence from a multi-century perspective," Applied Economics, Taylor & Francis Journals, vol. 52(10), pages 1070-1087, February.
    10. Tolga Omay & Furkan Emirmahmutoğlu, 2017. "The Comparison of Power and Optimization Algorithms on Unit Root Testing with Smooth Transition," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 623-651, April.
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    12. Tolga Omay & Dilem Yildirim, 2014. "Nonlinearity and Smooth Breaks in Unit Root Testing," Econometrics Letters, Bilimsel Mektuplar Organizasyonu (Scientific letters), vol. 1(1), pages 1-9.
    13. Tolga Omay & Furkan Emirmahmutoglu & Syed Jawad Hussain Shahzad, 2021. "Comparison of optimization algorithms for selecting the fractional frequency in Fourier form unit root tests," Applied Economics, Taylor & Francis Journals, vol. 53(7), pages 761-780, February.
    14. Tolga Omay & Burcu Ozcan & Muhammed Shahbaz, 2020. "Testing the hysteresis effect in the US state-level unemployment series," Journal of Applied Economics, Taylor & Francis Journals, vol. 23(1), pages 329-348, January.
    15. Ceyda Aktan & Perihan Iren & Tolga Omay, 2019. "Market development and market efficiency: evidence based on nonlinear panel unit root tests," The European Journal of Finance, Taylor & Francis Journals, vol. 25(11), pages 979-993, July.
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    17. Yifei Cai & Tolga Omay, 2022. "Using Double Frequency in Fourier Dickey–Fuller Unit Root Test," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 445-470, February.
    18. Tolga Omay & Mübariz Hasanov & Yongcheol Shin, 2018. "Testing for Unit Roots in Dynamic Panels with Smooth Breaks and Cross-Sectionally Dependent Errors," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 167-193, June.
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    23. Omay, Tolga, 2015. "Fractional Frequency Flexible Fourier Form to approximate smooth breaks in unit root testing," Economics Letters, Elsevier, vol. 134(C), pages 123-126.
    24. 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.
    25. Tolga Omay & Ayşegül Çorakcı & Furkan Emirmahmutoglu, 2017. "Real interest rates: nonlinearity and structural breaks," Empirical Economics, Springer, vol. 52(1), pages 283-307, February.
    26. Stephen Leybourne & Paul Newbold & Dimitrios Vougas, 1998. "Unit roots and smooth transitions," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 83-97, January.
    27. Shahbaz, Muhammad & Omay, Tolga & Roubaud, David, 2019. "Sharp and Smooth Breaks in Unit Root Testing of Renewable Energy Consumption: The Way Forward," MPRA Paper 92176, University Library of Munich, Germany, revised 11 Feb 2019.
    28. Esra Hasdemir & Tolga Omay & Zulal S Denaux, 2019. "Testing the Current Account Sustainability for BRICS Countries: Evidence from a Nonlinear Framework," Economics Bulletin, AccessEcon, vol. 39(1), pages 310-320.
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    Cited by:

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    5. 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.
    6. Romero-Ávila, Diego & Omay, Tolga, 2022. "Convergence of per capita energy consumption around the world: New evidence from nonlinear panel unit root tests," Energy Economics, Elsevier, vol. 111(C).

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