Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 179–205 | Cite as

Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models

  • Carole L. BirrellEmail author
  • David G. Steel
  • Yan-Xia Lin


Time series resulting from aggregation of several sub-series can be seasonally adjusted directly or indirectly. With model-based seasonal adjustment, the sub-series may also be considered as a multivariate system of series and the analysis may be done jointly. This approach has considerable advantage over the indirect method, as it utilises the covariance structure between the sub-series.

This paper compares a model-based univariate and multivariate approach to seasonal adjustment. Firstly, the univariate basic structural model (BSM) is applied directly to the aggregate series. Secondly, the multivariate BSM is applied to a transformed system of sub-series. The prediction mean squared errors of the seasonally adjusted aggregate series resulting from each method are compared by calculating their relative efficiency. Results indicate that gains are achievable using the multivariate approach according to the relative values of the parameters of the sub-series.

AMS Subject Classification

62M10 91B84 


Seasonal adjustment Basic structural model Kalman filter Multivariate time series State space model 


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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  • Carole L. Birrell
    • 1
    Email author
  • David G. Steel
    • 1
  • Yan-Xia Lin
    • 1
  1. 1.Centre for Statistical and Survey Methodology, School of Mathematics and Applied StatisticsUniversity of WollongongAustralia

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