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.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62H15 Hypothesis testing in multivariate analysis


Zbl 0699.62087