Abstract
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. In this paper we derive the resulting increase in the mean square of the l-step-ahead forecast error. We show 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 we find 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. Our conclusion concerning the width of the prediction intervals is different, however. Since outliers in a time series inflate the estimate of the innovation variance, we find that the estimated prediction intervals are quite sensitive to additive outliers.
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