Testing for a unit root with a nonlinear Fourier function

The paper develops a unit-root test that allows for an unknown number of structural breaks with unknown functional forms. The test is based on the fact that the behavior of such series can often be captured using a single frequency component of a Fourier approximation. Hence, instead of selecting specific break dates, the number of breaks, and the form of the breaks, the specification problem is transformed into selecting the proper frequency component to include in the estimating equation. Our proposed test does not exhibit any serious size distortions, and shows decent power. The appropriate use of the test is illustrated using real GDP and the interest rate differential.