A test for additive outliers applicable to long-memory time series

We propose a new test for additive outliers in Gaussian time series. The test statistic has a tractable asymptotic null distribution, namely the Gumbel distribution. It is calculated very simply without reference to parameters of any underlying model. The test is valid for a wide class of underlying stationary Gaussian series, and remains valid if the series being tested is pre-filtered by an invertible ARMA filter. To accelerate the convergence to the Gumbel distribution we introduce modified normalization constants and prove their validity. Simulation studies indicate that the test has reasonable power, comparable with a commonly used existing test.