Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2006-11-20 Number: 06-101/4 Author-Name: Siem Jan Koopman Author-Email: s.j.koopman@feweb.vu.nl Author-Workplace-Name: Vrije Universiteit Amsterdam Author-Name: Marius Ooms Author-Email: mooms@feweb.vu.nl Author-Workplace-Name: Vrije Universiteit Amsterdam Author-Name: Irma Hindrayanto Author-Email: ahindrayanto@feweb.vu.nl Author-Workplace-Name: Vrije Universiteit Amsterdam Title: Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment Abstract: This discussion paper led to an article in the Oxford Bulletin of Economics and Statistics (2009). Vol. 71, pages 683-713. See also (W.R. Bell, S.H. Holan & T.S. McElroy (Eds.)), 'Economic Time Series: Modeling and Seasonality', pages 3-35. London: Chapman and Hall/CRC Press. This paper discusses identification, specification, estimation and forecasting for a general class of periodic unobserved components time series models with stochastic trend, seasonal and cycle components. Convenient state space formulations are introduced for exact maximum likelihood estimation, component estimation and forecasting. Identification issues are considered and a novel periodic version of the stochastic cycle component is presented. In the empirical illustration, the model is applied to postwar monthly US unemployment series and we discover a significantly periodic cycle. Furthermore, a comparison is made between the performance of the periodic unobserved components time series model and a periodic seasonal autoregressive integrated moving average model. Moreover, we introduce a new method to estimate the latter model. Classification-JEL: C22; C51; E32; E37 Keywords: Unobserved component models; state space methods; seasonal adjustment; time–varying parameters; forecasting File-Url: https://papers.tinbergen.nl/06101.pdf File-Format: application/pdf File-Size: 475961 bytes Handle: RePEc:tin:wpaper:20060101