Seasonality in Univariate Unobserved Component Models

Four sources of seasonality are distinguished for quarterly time series: (i) seasonal unit roots, (ii) deterministic seasonal shifts, (iii) trending deterministic seasonals, and (iv) stationary stochastic seasonality. The identification of relevant UC models is discussed, including the role of a stationary seasonal lag term when the innovations are correlated. Methodologically, the importance of unit root testing for seasonal UC model specification is emphasized, with the proposed approach applied to quarterly U.S. government expenditure series.