Multivariate Trend-Cycle-Seasonal Decompositions with Correlated Innovations

Multivariate analysis can help to focus on important phenomena, including trend and cyclical movements, but any economic information in seasonality is typically ignored. The present paper aims to more fully exploit time series information through a multivariate unobserved component model for quarterly data that exhibits seasonality together with cross-variable component correlations. We show that economic restrictions, including common trends, common cycles and common seasonals can aid identification. The approach is illustrated using Italian GDP and consumption data.