On Outlier Detection in Time Series

SUMMARY The estimation and detection of outliers in a time series generated by a Gaussian auto-regressive moving average process is considered. It is shown that the estimation of additive outliers is directly related to the estimation of missing or deleted observations. A recursive procedure for computing the estimates is given. Likelihood ratio and score criteria for detecting additive outliers are examined and are shown to be closely related to the leave-k-out diagnostics studied by Bruce and Martin. The procedures are contrasted with those appropriate for innovational outliers.