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Exact maximum likelihood estimation for non-stationary periodic time series models

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  • Hindrayanto, Irma
  • Koopman, Siem Jan
  • Ooms, Marius

Abstract

Time series models with parameter values that depend on the seasonal index are commonly referred to as periodic models. Periodic formulations for two classes of time series models are considered: seasonal autoregressive integrated moving average and unobserved components models. Convenient state space representations of the periodic models are proposed to facilitate model identification, specification and exact maximum likelihood estimation of the periodic parameters. These formulations do not require a priori (seasonal) differencing of the time series. The time-varying state space representation is an attractive alternative to the time-invariant vector representation of periodic models which typically leads to a high dimensional state vector in monthly periodic time series models. A key development is our method for computing the variance-covariance matrix of the initial set of observations which is required for exact maximum likelihood estimation. The two classes of periodic models are illustrated for a monthly postwar US unemployment time series.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 11 (November)
Pages: 2641-2654

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Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2641-2654

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: State space methods Time-varying parameters SARIMA models Unobserved component models;

References

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  1. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
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  7. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  8. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521562607, April.
  9. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
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  11. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-66, October-D.
  12. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
  13. Jeremy Penzer & Yorghos Tripodis, 2007. "Single-season heteroscedasticity in time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 189-202.
  14. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2006. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Tinbergen Institute Discussion Papers 06-101/4, Tinbergen Institute.
  15. Gabriel Perez-Quiros & Margaret M. McConnell, 2000. "Output Fluctuations in the United States: What Has Changed since the Early 1980's?," American Economic Review, American Economic Association, vol. 90(5), pages 1464-1476, December.
  16. 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.
  17. Siem Jan Koopman & John A. D. Aston, 2006. "A non-Gaussian generalization of the Airline model for robust seasonal adjustment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 325-349.
  18. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 243-270.
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Citations

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Cited by:
  1. Boshnakov, Georgi N. & Lambert-Lacroix, Sophie, 2012. "A periodic Levinson-Durbin algorithm for entropy maximization," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 15-24, January.
  2. Dordonnat, Virginie & Koopman, Siem Jan & Ooms, Marius, 2012. "Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3134-3152.
  3. Bos, Charles S. & Koopman, Siem Jan & Ooms, Marius, 2014. "Long memory with stochastic variance model: A recursive analysis for US inflation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 144-157.

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