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Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment

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Author Info
Siem Jan Koopman
Marius Ooms
Irma Hindrayanto

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Abstract

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. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-0084.2009.00557.x
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Publisher Info
Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 71 (2009)
Issue (Month): 5 (October)
Pages: 683-713
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Handle: RePEc:bla:obuest:v:71:y:2009:i:5:p:683-713

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  2. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models I: time series ," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science. [Downloadable!]
  3. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Blackwell Publishing, vol. 26(4), pages 489-518, 07. [Downloadable!] (restricted)
  4. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, 08. [Downloadable!] (restricted)
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  5. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-27, January.
  6. Tommaso Proietti, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(2). [Downloadable!]
  7. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November. [Downloadable!] (restricted)
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  8. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  9. Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(6), pages 857-875, November. [Downloadable!] (restricted)
  10. Ooms, M. & Franses, Ph.H.B.F., 1998. "A seasonal periodic long memory model for monthly river flows," Econometric Institute Report EI 9842 Revision_Date: 20, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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