Detection and estimation of additive outliers in seasonal time series

The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.