The study proposes a multivariate unobserved components model in order to examine relationships at business cycle frequencies among macroeconomic variables. The series are decomposed into non-stationary trends, stationary cycles, and an irregular component. The co-movements among the particular cycles are modelled by a latent factor, whose dynamics is governed by a stochastic cycle. As a consequence of certain symmetry properties of the latter cyclical co-movement can be parametrized in terms of relative variances, phase shifts, and coherence. The model is applied to a U.S. labour market data set.
unobserved components models business cycles labour markets