Smooth break detection and de-trending in unit root testing

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Emirmahmutoğlu F., Omay T., Shahzad S. J. H., Nor S. M.

Mathematics, vol.9, no.4, pp.1-25, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3390/math9040371
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.1-25
  • Keywords: structural break, nonlinear unit root tests, flexible Fourier form, smooth transition regression, FLEXIBLE FOURIER FORM, ASYMMETRIC ADJUSTMENT, LEVEL, HYPOTHESIS, SERIES
  • Ankara Haci Bayram Veli University Affiliated: Yes


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.