Increasing seasonal variation; unit roots versus shifts in mean and trend

In this paper we consider model selection for time series with increasing (or decreasing) seasonal variation, where this variation can be described by (seasonal) unit root models with significant deterministic components or by models with less unit roots but with shifts in seasonal means or trends. As a model selection device we use tests based on the Osborn et al. regression, which we modify to allow for shifts in mean and trend. An application to disposable income in Japan yields that apparent unit roots are not robust to structural shifts induced by the Oil Crisis in the fourth quarter of 1973.