On outlier detection in time series.

*(English)*Zbl 0793.62048Summary: 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 |