A note on the Vogelsang test for additive outliers

The role of additive outliers in integrated time series has attracted some attention recently and research shows that outlier detection should be an integral part of unit root testing procedures. Recently, Vogelsang [1999. Two simple procedures for testing for a unit root when there are additive outliers. J. Time Ser. Anal. 20, 237–52] suggested an iterative procedure for the detection of multiple additive outliers in integrated time series. However, the procedure appears to suffer from serious size distortions towards the finding of too many outliers as has been shown by Perron and Rodriguez [2003. Searching for additive outliers in nonstationary time series. J. Time Ser. Anal. 24, 193–220] In this note we prove the inconsistency of the test in each step of the iterative procedure and hence alternative routes need to be taken to detect outliers in nonstationary time series.