Behavior of the standard Dickey-Fuller test when there is a Fourier-form break under the null hypothesis

- We assume that the null unit root process is with a Fourier component.
- We derive the asymptotic distribution of the standard Dickey-Fuller (DF) test.
- Asymptotic distributional results generate interesting predictions.
- The converse Perron phenomenon may occur when a Fourier-form break exists.
- The predictions are confirmed by simulation results.

We derive the null asymptotic distribution of the standard Dickey-Fuller test with the existence of an unnoticed Fourier component. The so-called converse Perron phenomenon might occur, but only in the trend-case with a low-frequency Fourier component and small error variance.