Locally Optimal Tests Against Seasonal Unit Roots.

This paper builds upon the existing literature on tests of the full hypothesis of deterministic seasonality in a univariate time-series process against the alternative of unit root behaviour at some or all of the zero and seasonal frequencies. Under the assumption of independent Gaussian errors we derive the class of locally weighed mean most powerful invariant tests against seasonal unit roots. We then propose both non-parametric and parametric modifications of these tests designed to have limit distributions which are free of nuisance parameters under weak conditions on the errors.