A seasonal unit roots test using the Fourier form to approximate smooth breaks

The present paper proposes a novel seasonal unit roots test considering a Fourier function to approximate smooth breaks. We suggest a seasonal unit roots testing procedure, as an extended version of the HEGY-type test that includes unknown multiple breaks. The empirical sizes of test statistics are generally close to nominal ones and the tests have good size properties. Additionally, the new seasonal unit roots test is superior to the traditional HEGY test in terms of power. As an empirical illustration of our test, we find out that the HEGY test fails to reject the null hypothesis of non-seasonal and seasonal unit roots because of not considering the smooth breaks, as expected. From this point, the empirical application supports and underlines the usefulness of our proposed seasonal unit roots test.