Seasonal unit root tests and flexible Fourier form

In this study, we propose a new seasonal unit root testing that incorporates the flexible Fourier form correction. This approach enhances the seasonal unit root testing procedure against nonlinearities and structural breaks without the need for additional testing. The proposed algorithm can handle these issues automatically. Additionally, we conduct simulation exercises to demonstrate that various forms of nonlinearities and smooth breaks can cause significant size distortions and power losses in standard seasonal unit root tests. However, the proposed approach largely corrects these issues and provides a robust alternative to standard tests under different forms of nonlinearities and structural breaks.