An outlier test for linear processes-II. Large contamination

Flak and Schmid introduced an outlier test for linear processes. The test statistic is based on a comparison of each observation with a one-step predictor. It was assumed that an upper bound for the total number of outliers sn is known, where n denotes the sample size. The asymptotic distribution of the test statistic was derived under the assumption that sn/n⇒0 and sn⇒• as n⇒•. This note deals with the asymptotic behaviour of this quantity, if sn/n⇒p0∈(0,1).