Tests for seasonal unit roots general to specific or specific to general?

In this paper the small sample properties of tests for seasonal unit roots in quarterly time series are evaluated and compared. The basic difference between the two tests is that the test proposed by Hylleberg, Engle, Granger, and Yoo (1990), the HEGY test, adopts the general to specific strategy and tests the null of a unit root, while the test proposed by Canova and Hansen (1993), the CH test, adopts the specific to general principle and tests the null of a stationary process around a deterministic seasonal pattern. The main result of the Monte Carlo experiments is that the two tests complement each other.