SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

Abstract

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.