Searching for Additive Outliers In Nonstationary Time Series¤

Recently, Vogelsang (1999) proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outliers in a given series. We show, via simulations, that under the null hypothesis of no outliers, it has the right size in ...nite samples to detect a single outlier but when applied in an iterative fashion to select multiple outliers, it exhibits severe size distortions towards ...nding an excessive number of outliers. We show that his iterative method is incorrect and derive the appropriate limiting distribution of the test at each step of the search. Whether corrected or not, we also show that the outliers need to be very large for the method to have any decent power. We propose an alternative method based on ...rst-di¤erenced data that has considerably more power. We also show that our method to identify outliers leads to unit root tests with more accurate ...nite sample size. The issues are illustrated using two US/Finland real-exchange rate series.