Smooth Break Detection and De-Trending in Unit Root Testing

Furkan Emirmahmutoğlu · Tolga Omay · Syed Jawad Hussain Shahzad · Safwan Mohd Nor

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

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.

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References

1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 2002Testing for a unit root in the nonlinear STAR framework 1988Testing Linearity Against Smooth Transition Autoregressive Models 1998Unit-Root Tests and Asymmetric Adjustment With an Example Using the Term Structure of Interest Rates 1981On the bias in flexible functional forms and an essentially unbiased form 2006A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks 2012The flexible Fourier form and Dickey–Fuller type unit root tests 2011A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks*

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