Analysis of the performance of test statistics for detection of Outliers (Additive, Innovative, Transient and Level Shift) in AR (1) processes

Outlier detection has always been of interest for researchers and data miners. It has been well researched in different knowledge and application domains. This study aims at exploring the correctly identifying outliers using most commonly applied statistics. We evaluate the performance of AO, IO, LS and TC as vulnerability to spurious outliers by means of empirical level of significance, power of the test indicating the sensitivity of the statistical tests in detecting changes and the vulnerability to masking of outliers in terms of misspecification frequencies are determined. We have observed that the sampling distribution of test statistic η_<i>tp</i>; <i>tp</i> = <i>AO</i>, <i>IO</i>, <i>LS</i>, <i>TC</i>  in case of AR(1) model is connected with the values of n and φ. The sampling distribution of  η_<i>TC</i>  is less concentrated than the sampling distribution of η_<i>AO</i>, η_<i>IO</i> and η_<i>LS</i>. In AR(1) process, empirical critical values for 1%, 5% and 10% upper percentiles are found to be higher than those generally used. We have also found the evidence that the test statistics for transient change (TC) needs to be revisited as the test statistics η_<i>TC</i> is found to be eclipsed by η_<i>AO</i>, η_<i>LS</i> and η_<i>IO</i> at different δ values. TC keeps on confusing with IO and AO, and at extreme δ values it just gets equal to AO and LS.