We suggest a new unit-root test with a Fourier function in the deterministic term in a Dickey–Fuller type regression framework. Our suggested test can complement the Fourier LM and DF-GLS unit root tests. They have good size and power properties.

We consider testing for the presence of nonlinearities in the mean and/or trend of a time series, approximating the potential nonlinear behaviour using a Fourier function expansion. In contrast to procedures that are currently available, we develop tests that are robust to the order of...