IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20100018.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/10018.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    2. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-436, July.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
    5. repec:cup:cbooks:9780521835954 is not listed on IDEAS
    6. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May.
    7. 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.
    8. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. C. Vladimir Rodr'iguez-Caballero & Esther Ruiz, 2024. "Temperature in the Iberian Peninsula: Trend, seasonality, and heterogeneity," Papers 2406.14145, arXiv.org.
    2. Fausto Hern'andez Trillo & C. Vladimir Rodr'iguez-Caballero & Daniel Ventosa-Santaul`aria, 2024. "Monopoly Unveiled: Telecom Breakups in the US and Mexico," Papers 2407.09695, arXiv.org.
    3. González-Rivera, Gloria & Rodríguez Caballero, Carlos Vladimir, 2023. "Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula," DES - Working Papers. Statistics and Econometrics. WS 37968, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Castillo-Manzano, José I. & Pedregal, Diego J. & Pozo-Barajas, Rafael, 2016. "An econometric evaluation of the management of large-scale transport infrastructure in Spain during the great recession: Lessons for infrastructure bubbles," Economic Modelling, Elsevier, vol. 53(C), pages 302-313.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Proietti, Tommaso & Pedregal, Diego J., 2023. "Seasonality in High Frequency Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 62-82.
    2. Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 47-69, January.
    3. 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.
    4. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
    5. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
    6. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, University Library of Munich, Germany.
    7. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    8. Koopman, Siem Jan & Ooms, Marius, 2006. "Forecasting daily time series using periodic unobserved components time series models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 885-903, November.
    9. Frits Bijleveld & Jacques Commandeur & Phillip Gould & Siem Jan Koopman, 2008. "Model‐based measurement of latent risk in time series with applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 265-277, January.
    10. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    11. Michele Caivano & Andrew Harvey & Alessandra Luati, 2016. "Robust time series models with trend and seasonal components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 99-120, March.
    12. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362, Edward Elgar Publishing.
    13. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    14. Paul Labonne & Martin Weale, 2018. "Temporal disaggregation of overlapping noisy quarterly data using state space models: Estimation of monthly business sector output from Value Added Tax data in the UK," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-18, Economic Statistics Centre of Excellence (ESCoE).
    15. Tommaso Proietti & Stefano Grassi, 2015. "Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search," Empirical Economics, Springer, vol. 48(3), pages 983-1011, May.
    16. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    17. Dimitrios Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Papers 0024, University of Peloponnese, Department of Economics.
    18. Martin Weale & Paul Labonne, 2022. "Nowcasting in the presence of large measurement errors and revisions," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2022-05, Economic Statistics Centre of Excellence (ESCoE).
    19. Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
    20. Stephen Pollock, 2014. "Trends Cycles and Seasons: Econometric Methods of Signal Extraction," Discussion Papers in Economics 14/04, Division of Economics, School of Business, University of Leicester.

    More about this item

    Keywords

    Frequency-specific model; Kalman filter; model-based seasonal adjustment; unobserved components time series model.;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20100018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.