Efficient Tests of the Seasonal Unit Root Hypothesis

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