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In many empirical studies concerning seasonal time series, it has been shown that the whole set of unit roots associated with seasonal random walks are not present. This article focuses on the overall F-tests for seasonal unit roots under some nonstationary alternatives different from the seasonal random walk. The asymptotic theory of these tests is established for these cases using a new approach based on circulant matrix concepts. The simulation results joined to this theoretic analysis showed that the overall F-tests, as well as their augmented versions, maintained high power against the nonstationary alternatives.

The Overall F-tests for Seasonal Unit Roots under Nonstationary Alternatives: Some Theoretical Results and a Monte Carlo Investigation