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Modeling Trigonometric Seasonal Components for Monthly Economic Time Series

Author

Listed:
  • Irma Hindrayanto

    (VU University Amsterdam)

  • John A.D. Aston

    (University of Warwick, UK)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Marius Ooms

    (VU University Amsterdam)

Abstract

This discussion paper led to an article in Applied Economics (2013). Vol. 45, pages 3024-3034. The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this paper we explore a generalisation 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 paper is two-fold. The first aim is to investigate the dynamic properties of this frequency specific basic structural model. The second aim is to relate the model to a comparable generalised version of the Airline model developed at the U.S. Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalised 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.

Suggested Citation

  • Irma Hindrayanto & John A.D. Aston & Siem Jan Koopman & Marius Ooms, 2010. "Modeling Trigonometric Seasonal Components for Monthly Economic Time Series," Tinbergen Institute Discussion Papers 10-018/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20100018
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    References listed on IDEAS

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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. 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 350-355, October.
    3. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    4. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-436, July.
    5. repec:cup:cbooks:9780521835954 is not listed on IDEAS
    6. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    7. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    8. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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