Smooth Break Detection and De-Trending in Unit Root Testing

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