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

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, June.
  2. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
  3. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  4. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York.
  5. Jeremy Penzer & Yorghos Tripodis, 2007. "Single-season heteroscedasticity in time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 189-202.
  6. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030, June.
  7. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
  8. Chang-Jin Kim & Charles R. Nelson & Jeremy M. Piger, 2003. "The less volatile U.S. economy: a Bayesian investigation of timing, breadth, and potential explanations," Working Papers 2001-016, Federal Reserve Bank of St. Louis.
  9. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 1998. "Tests for Forecast Encompassing," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 254-59, April.
  10. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, June.
  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. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
  13. 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.
  14. Anders Vredin & Anders Warne, 2000. "Unemployment and Inflation Regimes," Econometric Society World Congress 2000 Contributed Papers 0984, Econometric Society.
  15. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  16. 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.
  17. Matas-Mir, Antonio & Osborn, Denise R., 2004. "Does seasonality change over the business cycle? An investigation using monthly industrial production series," European Economic Review, Elsevier, vol. 48(6), pages 1309-1332, December.
  18. 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 36, Economics, The Univeristy of Manchester.
  19. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 243-270.
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