Testing Fractional Unit Roots with Non-linear Smooth Break Approximations using Fourier functions

In this paper we present a testing procedure for fractional orders of integration in the context of non-linear terms approximated by Fourier functions. The procedure is a natural extension of the linear method proposed in Robinson (1994) and similar to the one proposed in Cuestas and Gil-Alana (2016) based on Chebyshev polynomials in time. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper.