Koopman, S., Ooms, M. and Hindrayanto, A. (2009). Periodic unobserved cycles in seasonal time series with an application to U.S. unemployment Oxford Bulletin of Economics and Statistics, 71:683--713.

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, signal extraction and forecasting. The consequences for model-based seasonal adjustment are discussed. The new periodic model is applied to postwar monthly US unemployment series from which we identify a significant periodic stochastic cycle. A detailed periodic analysis is presented including a comparison between the performances of periodic and non-periodic UC models. {\textcopyright} Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009.