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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

    ()
    (Vrije Universiteit Amsterdam)

  • Marius Ooms

    ()
    (Vrije Universiteit Amsterdam)

  • Irma Hindrayanto

    ()
    (Vrije Universiteit Amsterdam)

Abstract

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-101/4.

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Date of creation: 20 Nov 2006
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Handle: RePEc:dgr:uvatin:20060101

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Web page: http://www.tinbergen.nl

Related research

Keywords: Unobserved component models; state space methods; seasonal adjustment; time–varying parameters; forecasting;

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  1. M Sensier & D van Dijk, 2003. "Testing for Volatility Changes in US Macroeconomic Time Series," Centre for Growth and Business Cycle Research Discussion Paper Series, Economics, The Univeristy of Manchester 36, Economics, The Univeristy of Manchester.
  2. Anders Vredin & Anders Warne, 2000. "Unemployment and Inflation Regimes," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0984, Econometric Society.
  3. Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 27(6), pages 857-875, November.
  4. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper, Federal Reserve Bank of Atlanta 2004-14, Federal Reserve Bank of Atlanta.
  5. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 26(4), pages 489-518, 07.
  6. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  7. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, Elsevier, vol. 123(1), pages 67-87, November.
  8. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 8(2), pages 1-22, May.
  9. 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, American Statistical Association, vol. 7(1), pages 117-27, January.
  10. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(3), pages 420-36, July.
  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, Elsevier, vol. 54(11), pages 2641-2654, November.
  2. Irma Hindrayanto & Jan Jacobs & Denise Osborn, 2014. "On trend-cycle-seasonal interactions," DNB Working Papers, Netherlands Central Bank, Research Department 417, Netherlands Central Bank, Research Department.

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