Alternative estimators and unit root tests for seasonal autoregressive processes

In this paper we suggest a new set of regression-based statistics for testing the seasonal unit root null hypothesis. The proposed tests are based on simple symmetric and weighted least squares estimation of the Hylleberg et al. (J. Econom. 44 (1990) 215) seasonal unit root test regression. We derive the asymptotic distributions of the new test statistics under both the seasonal unit root null hypothesis and under near seasonally integrated alternatives, from which we simulate the asymptotic local power functions of the new tests. The new tests are shown to dominate those of tests based on the existing statistics of Hylleberg et al. (J. Econom. 44 (1990) 215) in terms of asymptotic local power. Asymptotic critical values for the new tests are also provided. Monte Carlo simulation into the finite-sample size and power properties of the new tests for the case of quarterly data reveals that, overall, the new tests perform rather better than existing tests of the seasonal unit root hypothesis with the tests based on weighted symmetric least squares estimation being the most powerful of all.