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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)

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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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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/

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

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation

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  1. 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. [Downloadable!]
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  2. 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)
  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, 08. [Downloadable!] (restricted)
    Other versions:
  4. 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.
  5. 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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  6. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  7. 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)
  8. 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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