Smooth Break Detection and De-Trending in Unit Root Testing

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.

Signal Nonstationary Degree Evaluation Method Based on Moving Statistics Theory

“…ere are various methods in different fields to judge whether a given signal has nonstationarity or not and to evaluate the extent of nonstationarity, i.e., nonstationary degree. For example, unit root test method [16][17][18] and average entropy theory [19,20] are often used in econometrics. Recurrence plot [21][22][23][24] is usually used in nonlinear system analysis.…”

The Green Engine of Growth: Assessing the Influence of Renewable Energy Consumption and Environmental Policy on China’s Economic Sustainability

“…Furthermore, ϑ encapsulates the slope variable for the regression dummy, with D t being set to 1 for time periods post-breakpoint (t > T B ) and 0 otherwise, where T B is identified as the breakpoint. Emirmahmutoglu et al [143], Ilkay et al [144], Genç et al [145], and Ursavaş and Yilanci [146] elucidate the formulation of the Fourier-Augmented Dickey-Fuller and the Augmented Dickey-Fuller tests with structural breaks, presented in Equations ( 5) and ( 6), respectively. These estimations are refined through the application of an error-correction mechanism and the inclusion of an augmentation factor to address the intricacies of the unit root testing procedure.…”