A simulation study of additive outlier in ARMA (1, 1) model

Abnormal observation due to an isolated incident such as a recording error is known as additive outlier and it is often found in time series. Since extreme value of additive outliers may contribute to the inaccuracy of model specification, proper detection procedure is significant to avoid such error. Equations that explain the nature of an additive outlier and the test statistics pertaining to it are discussed in this article. This is followed by two separate simulation studies that are conducted to investigate the sampling behavior and detection performance of the test statistics in ARMA (1, 1) models. Results for the first simulation study show that the test statistics is an increasing function of sample size. Whilst in the other simulation study we see that the performance of the test statistics improves as large magnitudes of outlier effect are used.