Univariate and multivariate approaches to seasonal adjustment of aggregate series of different lengths

An aggregate series is a time series resulting from the aggregation of two or more sub-series. Two model-based approaches to seasonal adjustment of the aggregate series include a univariate and multivariate basic structural model. In a previous study [2], the variance of the seasonally adjusted series for the two approaches were compared using a range of true parameter values for a fixed length series. This paper compares the model-based univariate and multivariate approaches for different series lengths using the estimated parameters. A simulation study compares two outcomes: the accuracy of the estimated parameters of the aggregate series, and the naïve bias in the prediction error variance. The results show that for the two cases studied, the use of the multivariate approach in the estimation of parameters improves the accuracy of the parameter estimates of the aggregated series. This was especially true for short to medium length time series. The relative efficiencies of the seasonally adjusted aggregated series also showed good gains for the multivariate model. For one of the cases, there was a substantial decrease in the naïve bias with the use of the multivariate model. Bias correction is also discussed for the two approaches.