Trend-cycle-seasonal interactions: identification and estimation

Economists typically use seasonally adjusted data in which the assumption is imposed
that seasonality is uncorrelated with trend and cycle. The importance of this assumption
has been highlighted by the Great Recession. The paper examines an unobserved
components model that permits non-zero correlations between seasonal and nonseasonal
shocks. Identification conditions for estimation of the parameters are discussed
from the perspectives of both analytical and simulation results. Applications to UK
household consumption expenditures and US employment reject the zero correlation
restrictions and also show that the correlation assumptions imposed have important
implications about the evolution of the trend and cycle in the post-Great Recession
period.