Fractional Frequency Flexible Fourier Form to approximate smooth breaks in unit root testing

- Fractional Frequency Flexible Fourier Form-DF-type of unit root test is proposed.
- The small sample properties of FFFFF-DF-type test are better than EL test.
- FFFFF-DF-type test improves the empirical testing performance.
- FFFFF-DF-type test prevents type two errors and over-filtration problems.

In this study, a Fractional Frequency Flexible Fourier Form DF-type unit root test is proposed. The small sample properties of the proposed test are found to be better than that of the integer frequency counterpart.