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On outlier detection in time series. (English) Zbl 0793.62048

Summary: The estimation and detection of outliers in a time series generated by a Gaussian autoregressive 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 A. G. Bruce and R. D. Martin [ibid. 51, No. 3, 363-424 (1989; Zbl 0699.62087)]. The procedures are contrasted with those appropriate for innovational outliers.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62H12 Multivariate estimation 62H15 Multivariate hypothesis testing