Unobserved Components in Univariate Series

  • Víctor Gómez
Part of the Statistics and Computing book series (SCO)


As mentioned in Gómez and Maravall (Seasonal adjustment and signal extraction in economic time series. In: Peña D, Tiao GC, Tsay RS (eds), A course in time series analysis, (chap 8). Wiley, New York, 2001), there exist at present two approaches to the problem of specifying a model in which several unobserved components that follow ARIMA models are present. The first one begins by specifying directly the models for the components and is called the structural time series approach. The other approach, called the ARIMA model based (AMB) method, starts by identifying a model for the observed series and derives from it the appropriate models for the components.


  1. Bell, W. R., & Hillmer, S. C. (1984). Issues involved with the seasonal adjustment of economic time series. Journal of Business & Economic Statistics,2, 291–320.Google Scholar
  2. Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis: Forecasting and control (rev. ed.). San Francisco: Holden-Day.zbMATHGoogle Scholar
  3. Box, G. E. P., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association,70, 70–79.MathSciNetCrossRefGoogle Scholar
  4. Butterworth, S. (1930). On the theory of filter amplifiers. Experimental Wireless and the Wireless Engineer,7, 536–541.Google Scholar
  5. De Livera, A. M., Hyndman, R. J., & Snyder, R. D. (2011). Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American Statistical Association,106, 1513–1527.MathSciNetCrossRefGoogle Scholar
  6. Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods (2nd ed.). Oxford: Oxford University Press.CrossRefGoogle Scholar
  7. Gómez, V. (2001). The use of butterworth filters for trend and cycle estimation in economic time series. Journal of Business and Economic Statistics,19, 365–373.MathSciNetCrossRefGoogle Scholar
  8. Gómez, V. (2016). Multivariate time series models with linear state space structure. New York: Springer.zbMATHGoogle Scholar
  9. Gómez, V., & Maravall, A. (2001a). Programs TRAMO and SEATS, instructions for the user (Beta Version: June 1997) (Working Paper No. 97001). Dirección General De Presupuestos, Ministry of Finance, Madrid, Spain.Google Scholar
  10. Gómez, V., & Maravall, A. (2001b). Seasonal adjustment and signal extraction in economic time series. In D. Peña, G. C. Tiao, & R. S. Tsay (Eds.), A course in time series analysis (chap. 8). New York: Wiley.Google Scholar
  11. Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge University Press.Google Scholar
  12. Harvey, A. C. (1993). Time series models (2nd ed.). Hemel Hempstead: Harvester Wheatsheaf.zbMATHGoogle Scholar
  13. Hillmer, S. C., & Tiao, G. C. (1982). An ARIMA–model–based approach to seasonal adjustment. Journal of the American Statistical Association,77, 63–70.MathSciNetCrossRefGoogle Scholar
  14. Hodrick, R. J., & Prescott, E. C. (1997). Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit and Banking,29, 1–16.CrossRefGoogle Scholar
  15. Oppenheim, A. V., & Schafer, R. W. (1989). Discrete–time signal processing. Englewood Cliffs: Prentice Hall.zbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Víctor Gómez
    • 1
  1. 1.General Directorate of BudgetsMinistry of Finance and Public AdministrationsMadridSpain

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