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

Ljung, Greta M.

J. R. Stat. Soc., Ser. B 55, No. 2, 559-567 (1993).

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. in statistics (GARCH)
62H12	Estimation in multivariate analysis
62H15	Hypothesis testing in multivariate analysis

Keywords:

leave-\(k\)-out diagnostics; interpolation; likelihood function; outlier detection; studentized residuals; time series; Gaussian autoregressive moving average process; estimation of additive outliers; estimation of missing or deleted observations; recursive procedure; score criteria; innovational outliers

Citations:

Zbl 0699.62087