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.
Highlights
Macroeconomic variables are subject to either smooth or sharp structural breaks e.g., great moderation since the mid-1980s or the 2007–09 global financial crisis
The unit root tests that employ a flexible Fourier function to model the structural breaks (Enders and Lee [1,2]) have attracted a great deal of attention compared to the tests employing the smooth transition (ST) function
We show that the Fourier function may lead to an over-filtration problem when structural break and non-linearity are simultaneously present in the data
Summary
Macroeconomic variables are subject to either smooth or sharp structural breaks e.g., great moderation since the mid-1980s or the 2007–09 global financial crisis. Their claim that the KSS test is a rival of their testing procedure can still be understood when the results of their simulation experiments on different functional forms are considered From their simulation experiments, it can be seen that the Fourier function can imitate any kind of series’ structure as well as statedependent non-linearity by using the low-frequency component, but this phenomenon is not explained explicitly in their study. ( EL) test is found to have better power performance than the FKSS unit root test in this DGP setting This contradiction is the main concern of our paper that the FFF methodology has some over-filtration problem while detecting the structural break even with its low frequency component k = 1. FKSS test has better power performance in a state-dependent non-linear DGP with its two components, the FFF and ESTAR non-linearity This unexpected result is further investigated in the simulation analysis.
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