Analysis of the performance of test statistics for detection of outliers (additive, innovative, transient, and level shift) in AR (1) processes

ABSTRACT

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 (ELS), 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_tp; tp = AO, IO, LS, TC  in case of AR(1) model is connected with the values of n and φ. The sampling distribution of  η_TC  is less concentrated than the sampling distribution of η_AO, η_IO, and η_LS. 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_TC is found to be eclipsed by η_AO, η_LS and η_IO 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.

KEYWORDS:

• Chen and Liu procedure
• Discordant observations
• IO/TC/AO/LS
• Simulation analysis
• Structural breaks

JEL CLASSIFICATION:

• C15
• C18
• C63
• C32
• C87

Notes

1 The simulation analysis is conducted by formulating code in R-CRAN. The code can be obtained from authors on request.

2 Sampling distribution of in the presence of one outlier stating: detail simulation results from tables comprising w = 3sigma can be obtained from the authors.

3 On using 5000 iterations the results for c = 4 have very little impact as compared to N = 1000 iterations done earlier.

4 Detail Tables showing the patterns in empirical Power of test statistics are available from the authors.

5 Tables showing behavior of delta values in Transient change detection are available from the authors on demand.