Parameter estimation and naïve bias for a seasonally adjusted aggregate series of different lengths using univariate and multivariate approaches

An aggregate series is a time series resulting from the aggregation of two or more sub-series. This paper compares a model-based univariate and multivariate approach to seasonal adjustment of the aggregate series for different series lengths. A simulation study compares two outcomes: the accuracy of the estimated parameters of the aggregate series, and the naive bias in the prediction error variance. The results show that for the two examples 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 the case 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 examples, there was a substantial decrease in the naive bias with the use of the multivariate model.