Open AccessSACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier
Author(s) -
R. Suresh
Publication year - 2021
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2021/v14i130320
Subject(s) - autoregressive model , autocorrelation , outlier , autoregressive–moving average model , series (stratigraphy) , mathematics , white noise , moving average model , statistics , star model , moving average , time series , noise (video) , lag , econometrics , autoregressive integrated moving average , computer science , artificial intelligence , paleontology , computer network , image (mathematics) , biology
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.