This paper investigates business cycle relations among different economies in the Euro area. Cyclical dynamics are explicitly modelled as part of a time series model. We introduce mechanisms that allow for increasing or diminishing phase shifts and for time-varying association patterns in...

Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide confidence intervals around the seasonally...

We introduce a general class of periodic unobserved component (UC) time series models with stochastic trend and seasonal components and with a novel periodic stochastic cycle component. The general state space formulation of the periodic model allows for exact maximum likelihood estimation,...