Assume that a time series of length n=T+k includes an additive outlier at time T and suppose this fact is ignored in the estimation of the coefficients and the calculation of the forecasts. This paper derives the resulting increase in the mean square of the l-step-ahead forecast error. It shows that this increase is due to (i) a carry-over effect of the outlier on the forecast, and (ii) a bias in the estimates of the autoregressive and moving average coefficients. Looking at several special cases it is found that this increase is rather small provided that the outlier occurs not too close to the forecast origin. In such cases the point forecasts are largely unaffected. The conclusion concerning the width of the prediction intervals is different, however. Since outliers in a time series inflate the estimate of the innovation variance, the estimated prediction intervals are found to be quite sensitive to additive outliers.
