The Behaviour of Seasonal Unit Root Tests for Quarterly Time Series with Seasonal Mean Shifts

This paper studies the behaviour of the HEGY tests for quarterly data, for seasonal autoregressive unit roots, when the time series being analysed is deterministic seasonal stationary but exhibits a change in the seasonal pattern. As a by-product, we also analyse the HEGY tests for the nonseasonal unit root when the data generation process is also trend stationary. Our results show that, asymptotically, at least when the break magnitudes are finite, the HEGY test statistics are not biased towards the acceptance of the seasonal and nonseasonal unit root hypotheses. Just under some combinations of the parameters a larger sample size may be required to preserve the power properties of the tests. Hence, our results are also useful to understand and to predict the finite sample power performance of the test statistics under several circumstances