Seasonal adjustment of aggregate series using univariate and multivariate basic structural models

Government statistical agencies are required to seasonally adjust non-stationary time series resulting from an aggregate of a number of cross-sectional time series. Traditionally, this has been achieved using the X-11 or X12-ARIMA process by us- ing either direct or indirect seasonal adjustment. However, neither of these methods utilizes the multivariate system of time series which underlies the aggregate series. This paper compares a model-based univariate approach to seasonal adjustment with a model-based multivariate approach. Firstly, the univariate basic structural model (BSM) is applied directly to the aggregate series to obtain estimates of the seasonal components. Secondly, the multivariate basic structural model is applied to a trans- formed system of cross-sectional series to also obtain estimates of the seasonal com- ponents of the aggregate series. The prediction mean squared errors resulting from each method are compared by calculating their relative e±ciency. An experimental study is conducted which ¯xes the parameters of the aggregate series and varies the stochastic structure of two cross-sectional series. It is shown that gains are achievable using the multivariate approach under certain conditions which rely on the relative values of the parameters within and between components of the cross-sectional series.