Estimation of Time Series Parameters in the Presence of Outliers

Outliers in time series can be regarded as being generated by dynamic intervention models at unknown time points. Two special cases, innovational outlier (IO) and additive outlier (AO), are studied in this article. The likelihood ratio criteria for testing the existence of outliers of both types, and the criteria for distinguishing between them are derived. An iterative procedure is proposed for detecting IO and AO in practice and for estimating the time series parameters in autoregressive-integrated-moving-average models in the presence of outliers. The powers of the procedure in detecting outliers are investigated by simulation experiments. The performance of the proposed procedure for estimating the autoregressive coefficient of a simple AR(l) model compares favorably with robust estimation procedures proposed in the literature. Two real examples are presented.