On Trend-Cycle-Seasonal Interactions

Abstract

Traditional unobserved component models assume that the trend, cycle and seasonal components of an individual time series evolve separately over time. Although this assumption has been relaxed in recent papers that focus on trend-cycle interactions, it remains at the core of all seasonal adjustment methods applied by official statistical agencies around the world. The present paper develops an unobserved components model that permits non-zero correlations between seasonal and non-seasonal shocks, hence allowing testing of the uncorrelated assumption that is traditionally imposed. Identification conditions for estimation of the parameters are discussed, while applications to observed time series illustrate the model and its implications for seasonal adjustment.

Keywords: trend-cycle-seasonal decomposition, unobserved components, state-space models, seasonal adjustment, global real economic activity, unemployment

JEL Classification: C22, E24, E32, E37, F01