Seasonal integration and the evolving seasonals model

The paper uses a model of seasonality popular in the 1960s, the evolving seasonals model, to explore issues relating to testing for unit roots in seasonal time series. The model is used to show how data can be transformed in such a way that tests for seasonal integration simply become those for regular unit roots. Once this connection is established it becomes obvious that there are many possible ways of constructing a test for seasonal integration, only a few of which have appeared in the literature. A byproduct of the approach is the separation of the existence of a seasonal pattern from its nature allowing one to place developments such as fractionally integrated and periodic seasonality within the same framework as regular integration.