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Modelling trigonometric seasonal components for monthly economic time series

  • Irma Hindrayanto
  • John A.D. Aston
  • Siem Jan Koopman
  • Marius Ooms

The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this article, we explore a generalization of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the article is two-fold. The first aim is to investigate the dynamic properties of this frequency-specific Basic Structural Model (BSM). The second aim is to relate the model to a comparable generalized version of the Airline model developed at the US Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalized models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models.

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File URL: http://hdl.handle.net/10.1080/00036846.2012.690937
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Article provided by Taylor & Francis Journals in its journal Applied Economics.

Volume (Year): 45 (2013)
Issue (Month): 21 (July)
Pages: 3024-3034

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Handle: RePEc:taf:applec:v:45:y:2013:i:21:p:3024-3034
DOI: 10.1080/00036846.2012.690937
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  1. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
  2. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
  3. Maravall, Agustin, 1985. "On Structural Time Series Models and the Characterization of Components," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 350-55, October.
  4. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(04), pages 988-1009, August.
  5. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, December.
  6. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
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