Consistent Multivariate Seasonal Adjustment for Gross Domestic Product and its Breakdown in Expenditures

R. Bikker*, Jan van den Brakel, P. Ouwehand, R. van der Stegen, S. Krieg

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Seasonally adjusted series of Gross Domestic Product (GDP) and its breakdown in underlying categories or domains are generally not consistent with each other. Statistical differences between the total GDP and the sum of the underlying domains arise for two reasons. If series are expressed in constant prices, differences arise due to the process of chain linking These differences increase if, in addition, a univariate seasonal adjustment, with for instance X-13ARIMA-SEATS, is applied to each series separately. In this article, we propose to model the series for total GDP and its breakdown in underlying domains in a multivariate structural time series model, with the restriction that the sum over the different time series components for the domains are equal to the corresponding values for the total GDP. In the proposed procedure, this approach is applied as a pretreatment to remove outliers, level shifts, seasonal breaks and calendar effects, while obeying the aforementioned consistency restrictions. Subsequently, X-13ARIMA-SEATS is used for seasonal adjustment. This reduces inconsistencies remarkably. Remaining inconsistencies due to seasonal adjustment are removed with a benchmarking procedure.

Original languageEnglish
Pages (from-to)9-30
Number of pages22
JournalJournal of Official Statistics
Issue number1
Early online date26 Mar 2019
Publication statusPublished - Mar 2019


  • Seasonal adjustment
  • discrepancies
  • Kalman filter
  • multivariate structural time series models
  • benchmarking

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