Using Double Frequency in Fourier Dickey–Fuller Unit Root Test

We propose a double frequency fourier Dickey–Fuller (DF) unit root test. The asymptotic theory of the newly proposed test is first presented in this study. We conduct a series of simulations which suggest the proposed test statistic has correct size performance and gains more power when breaks are located at the beginning and end of the sample and in smooth type. In empirical analysis, we utilize the new test to examine the unit root hypothesis of relative commodity prices measured by Harvey et al. (Rev Econ Stat 92(2):367–377, 2010). The empirical results show that more relative commodity prices are stationary around a deterministic trend generated from double frequency Fourier function.