ABSTRACT
As in other fields of statistics, the presence of outliers can present serious problems in time series modeling. There are two types of outliers in time series. We have the innovation outliers (IO) if the noise process at has a heavy tailed distribution compared with the normal distribution. This type of outlier is less problematic if at has finite fourth order moment. It can be shown that in this situation the conditional least squares estimators obtained by minimizing (2.3b) will still be consistent with the same covariance matrix given by the inverse of I in (2.5). Another more serious type of outliers is known as the additive outliers (AO). Additive outliers are present if instead ofXt we observe zt = Xt+Wt, where {Xt} follow the ARMA time series (2.1), and Wt is a contaminating process with P (Wt = 0) = C for some C with 0 ≤ C ≤ 1. The presence of Wt masks the original autocorrelation structure of Xt and hence causes greater problems in the modeling of Xt. Note that in many applications Wt is assumed to be independent, identically distributed, and sometimes assumes a fixed value δ.
