The effect of additive outliers on the estimates from aggregated and disaggregated ARIMA models

Assume that the observed series follows an ARIMA process, and that the forecaster is only interested in predicting aggregated values. In this case the aggregate series also follows an ARIMA process and the prediction could be done using either the disaggregate or the aggregate models. The paper derives the approximate expected values of the estimates of the model coefficients and of the innovation variances in the presence of a single additive outlier. The approximations are also checked through simulations. The present conclusion is that the approximation is good, provided the size of the series is not too small, and that the additive outlier can have a stronger effect on the disaggregate model than on the aggregate model. An empirical analysis is presented using the international airline passengers series.