Variance ratio tests of the seasonal unit root hypothesis

In this paper we develop tests of the seasonal (quarterly) unit root null hypothesis which reject in favour of stationarity for small values of certain variance ratio statistics, similar to those used by Canova and Hansen (J. Bus. Econom. Statist. 13 (1995) 237) in a different testing context. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives even when we allow for the possibility of both weak dependence and periodically heteroscedastic behaviour in the driving shocks. This is in contrast to the popular regression-based lag-augmented seasonal unit root tests of Hylleberg et al. (J. Econometrics 44 (1990) 215). A simulation study into the finite sample size and power properties of our proposed tests suggests that they display far superior size properties and, overall, broadly comparable power properties to the corresponding tests of Hylleberg et al. (J. Econometrics 44 (1990) 215), implemented with data-based lag augmentation. The results for the variance ratio tests at the seasonal harmonic frequency are particularly encouraging.