Efficient Tests of the Seasonal Unit Root Hypothesis

In this paper we derive, under the assumption of Gaussian errors with known error covariance matrix, asymptotic local power bounds for seasonal unit root tests for both known and unknown deterministic scenarios and for an arbitrary seasonal aspect. We demonstrate that the optimal test of a unit root at a given spectral frequency behaves asymptotically independently of whether unit roots exist at other frequencies or not. We also develop modified versions of the optimal tests which attain the asymptotic Gaussian power bounds under much weaker conditions. We further propose near-efficient regression-based seasonal unit root tests using pseudo-GLS de-trending and show that these have limiting null distributions and asymptotic local power functions of a known form. Monte Carlo experiments indicate that the regression-based tests perform well in finite samples.