Outlier detection in ARIMA and seasonal ARIMA models by Bayesian Information Type Criteria Pedro Galeano and Daniel Pe˜ na Departamento de Estad´ ıstica Universidad Carlos III de Madrid 1 Introduction The detection of outliers in a time series is an important issue because their presence may have serious effects on the analysis in many different ways. For instance, even if the time series model is well specified, outliers can lead to biased parameter estimation, which may derives in poor forecasts. Several outlier detection procedures have been proposed for detecting different outlier types in autoregressive integrated and moving average (ARIMA) time series models, including the ones proposed in Fox (1972), Tsay (1986, 1988), Chang, Tiao and Chen (1988), Chen and Liu (1993), McCulloch and Tsay (1994), Le, Martin and Raftery (1996), Luce˜ no (1998), Justel, Pe˜ na and Tsay (2001), Bianco, Garcia-Ben, Mart´ ınez and Yohai (2001) and S´anchez and Pe˜ na (2003), among others. Most of these methods are based on sequential detection procedures that test for the presence of an outlier, and if one outlier is found, its size is estimated, its effect is cleaned from the series and a new search for outliers is started. However, sequential detection procedures find several drawbacks. First, in many situations, the distribution of the test statistics are unknown and critical values needed to apply the tests are obtained via simulation for different sample sizes and models. Second, the masking effect, which means that outliers are undetected because of the presence of others. Third, the swamping effect, which means that outliers affect the data in such a way that good observations appear to be outliers as well. Finally, iterative procedures sequentially test for the presence of outliers which usually leads to overdetect the number of outliers due to the multiple testing problem. The main purpose of this paper is to develop an outlier detection procedure for additive outliers in ARIMA and seasonal ARIMA time series models, which tries to mitigate the effects due to the drawbacks of 1