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Seasonality with Trend and Cycle Interactions in Unobserved Components Models

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  • Siem Jan Koopman

    ()
    (VU University Amsterdam)

  • Kai Ming Lee

    ()
    (VU University Amsterdam)

Abstract

Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance, and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. In this paper, we formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle dependent seasonal fluctuations.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-028/4.

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Date of creation: 00 0000
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Handle: RePEc:dgr:uvatin:20080028

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Keywords: Seasonal interaction; Unobserved components; Non-linear state space models;

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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, University of Oxford, Department of Economics 1998-W06, University of Oxford, Department of Economics.
  2. 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, Elsevier, vol. 48(6), pages 1309-1332, December.
  3. Franses Philip Hans & de Bruin Paul, 2000. "Seasonal Adjustment and the Business Cycle in Unemployment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 4(2), pages 1-14, July.
  4. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, Elsevier, vol. 16(2), pages 247-260.
  5. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(2), pages 127-52, April.
  6. Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper, Tilburg University, Center for Economic Research 1998-142, Tilburg University, Center for Economic Research.
  7. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 1(3), pages 253-64, July.
  8. Andrew C Harvey & Andrew Scott, 1994. "Seasonality in Dynamic Regression Models," CEP Discussion Papers, Centre for Economic Performance, LSE dp0184, Centre for Economic Performance, LSE.
  9. S. J. Koopman & J. Durbin, 2003. "Filtering and smoothing of state vector for diffuse state-space models," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 24(1), pages 85-98, 01.
  10. repec:fth:erroem:9923/a is not listed on IDEAS
  11. Cecchetti, Stephen G & Kashyap, Anil K & Wilcox, David W, 1997. "Interactions between the Seasonal and Business Cycles in Production and Inventories," American Economic Review, American Economic Association, American Economic Association, vol. 87(5), pages 884-92, December.
  12. Commandeur, Jacques J.F. & Koopman, Siem Jan, 2007. "An Introduction to State Space Time Series Analysis," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199228874, October.
  13. Franses, Philip Hans, 1995. "Quarterly US Unemployment: Cycles, Seasons and Asymmetries," Empirical Economics, Springer, Springer, vol. 20(4), pages 717-25.
  14. Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 30(1), pages 47-69, 01.
  15. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
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Cited by:
  1. Sumru Altug & Cem Cakmakli, 2014. "Inflation Targeting and Inflation Expectations: Evidence for Brazil and Turkey," Koç University-TUSIAD Economic Research Forum Working Papers, Koc University-TUSIAD Economic Research Forum 1413, Koc University-TUSIAD Economic Research Forum.
  2. Steven Clark & T. Coggin, 2009. "Trends, Cycles and Convergence in U.S. Regional House Prices," The Journal of Real Estate Finance and Economics, Springer, Springer, vol. 39(3), pages 264-283, October.

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