A simple diagnostic method of outlier detection for stationary Gaussian time series

In this paper we present a "model free' method of outlier detection for Gaussian time series by using the autocorrelation structure of the time series. We also present a graphic diagnostic method in order to distinguish an additive outlier (AO) from an innovation outlier (IO). The test statistic for detecting the outlier has a χ ² distribution with one degree of freedom. We show that this method works well when the time series contain either one type of the outliers or both additive and innovation type outliers, and this method has the advantage that no time series model needs to be estimated from the data. Simulation evidence shows that different types of outliers can be graphically distinguished by using the techniques proposed.