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Transformations and seasonal adjustment

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  • Tommaso Proietti
  • Marco Riani

Abstract

. We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, measured on a ratio scale, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series admit an analytic finite representation only for particular values of the transformation parameter, e.g. for a fractional Box–Cox transformation parameter. Even if available, the analytical derivation can be tedious and difficult. As an alternative we propose to compute the two conditional moments of the seasonally adjusted series by means of numerical and Monte Carlo integration. The former is both fast and reliable in univariate applications. The latter uses the algorithm known as the ‘simulation smoother’ and it is most useful in multivariate applications. We present two case studies dealing with robust seasonal adjustment under the square root and the fourth root transformation. Our overall conclusion is that robust seasonal adjustment under transformations is feasible from the computational standpoint and that the possibility of transforming the scale ought to be considered as a further option for improving the quality of seasonal adjustment.

Suggested Citation

  • Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 47-69, January.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:1:p:47-69
    DOI: 10.1111/j.1467-9892.2008.00600.x
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    References listed on IDEAS

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    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. Riani Marco, 2004. "Extensions of the Forward Search to Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
    3. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    4. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    5. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    6. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    7. Harvey, Andrew & Proietti, Tommaso (ed.), 2005. "Readings in Unobserved Components Models," OUP Catalogue, Oxford University Press, number 9780199278695.
    8. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    9. 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, vol. 16(2), pages 127-152, April.
    10. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    11. 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.
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    Cited by:

    1. Siem Jan Koopman & Kai Ming Lee, 2009. "Seasonality with trend and cycle interactions in unobserved components models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 427-448, September.
    2. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    3. Behm, Svenia & Haupt, Harry, 2020. "Predictability of hourly nitrogen dioxide concentration," Ecological Modelling, Elsevier, vol. 428(C).
    4. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    5. Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2023. "Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 75-102, March.
    6. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    7. Atkinson, Anthony C. & Riani, Marco & Corbellini, Aldo, 2021. "The box-cox transformation: review and extensions," LSE Research Online Documents on Economics 103537, London School of Economics and Political Science, LSE Library.

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