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

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 e±ciency. Results indicate that gains are achievable using the multivariate approach according to the relative values of the parameters of the sub-series.