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 unit root tests at the zero and seasonal frequencies 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. Optimal tests for unit roots at multiple frequencies are also developed. We also detail 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 local GLS de-trending which, in the case of single frequency unit root tests, are shown to have limiting null distributions and asymptotic local power functions of a known form. Monte Carlo simulations indicate that these tests perform well in finite samples.