The Behavior of HEGY Tests for Quarterly Time Series with Seasonal Mean Shifts

Abstract

This paper studies the behavior of the HEGY statistics for quarterly data, for seasonal autoregressive unit roots, when the analyzed time series is deterministic seasonal stationary but exhibits a change in the seasonal pattern. As a by-product we analyze also the HEGY test for the nonseasonal unit root, the data generation process being trend stationary too. Our results show that when the break magnitudes are finite the HEGY test statistics are not asymptotically biased towards the non-rejection of the seasonal and nonseasonal unit root hypotheses. However, the finite sample power properties may be substancially affected, the behavior of the tests depending on the type of the break. Hence, our results are also useful to understand and to predict this behavior under several circumstances.seasonality; unit roots; strctural breaks; HEGY tests