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

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  • Siem Jan Koopman
  • Marius Ooms
  • Irma Hindrayanto

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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Bibliographic 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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  1. Anders Vredin & Anders Warne, 2000. "Unemployment and Inflation Regimes," Econometric Society World Congress 2000 Contributed Papers 0984, Econometric Society.
  2. Robert Taylor & Peter Burridge, 2004. "Bootstrapping the HEGY Seasonal Unit Root Tests," Econometric Society 2004 North American Summer Meetings 125, Econometric Society.
  3. 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, August.
  4. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  5. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, 07.
  6. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  7. Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 857-875, November.
  8. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
  9. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May.
  10. 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.
  11. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
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Cited by:
  1. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
  2. Irma Hindrayanto & Jan Jacobs & Denise Osborn, 2014. "On trend-cycle-seasonal interactions," DNB Working Papers 417, Netherlands Central Bank, Research Department.

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