Sequential Outlier Detection in Nonstationary Time Series

A novel method for sequential outlier detection in nonstationary time series is proposed. The method tests the null hypothesis of “no outlier” at each time point, addressing the multiple testing problem by bounding the error probability of successive tests, using extreme‐value theory. The asymptotic properties of the test statistic are studied under the null hypothesis and alternative hypothesis. The finite sample properties of the new detection scheme are investigated by means of a simulation study, and the method is compared with alternative procedures that have recently been proposed in the statistics and machine learning literature.