Seasonal Adjustment of Aggregated Series using Univariate and Multivariate Basic Structural Models

Government statistical agencies are required to seasonally adjust non-stationary time series resulting from aggregation of a number of cross-sectional time series. Traditionally, this has been achieved using the X-11 or X12-ARIMA process by using either direct or indirect seasonal adjustment. However, neither of these methods utilizes the multivariate system of time series which underlies the aggregated series. This paper compares a model-based univariate approach to seasonal adjustment with a modelbased multivariate approach. Firstly, the univariate basic structural model (BSM) is applied directly to the aggregated series to obtain estimates of the seasonal components. Secondly, the multivariate basic structural model is applied to a transformed system of cross-sectional series to also obtain estimates of the seasonal components of the aggregated series. The prediction mean squared errors 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 cross-sectional series.