Heteroscedasticity testing after outlier removal

Abstract

Given the effect that outliers can have on regression and specification testing, a vastly used robustification strategy by practitioners consists in: (i) starting the empirical analysis with an outlier detection procedure to deselect atypical data values; then (ii) continuing the analysis with the selected non-outlying observations. The repercussions of such robustifying procedure on the asymptotic properties of subsequent inferential procedures are, however, underexplored. We study the effects of such a strategy on testing for heteroscedasticity. Specifically, using weighted and marked empirical processes of residuals theory, we show that the White test implemented after the outlier detection and removal is asymptotically chi-square if the underlying errors are symmetric. In a simulation study, we show that—depending on the type of outliers—the standard White test can be either severely undersized or oversized, as well as have trivial power. The statistic applied after deselecting outliers has good finite sample properties under symmetry but can suffer from size distortions under asymmetric errors. Given these results, we devise an empirical modeling strategy to guide practitioners whose preferred approach is to remove outliers from the sample.

Keywords:

• Asymptotic theory
• heteroscedasticity
• marked and weighted empirical processes
• outlier detection
• robust statistics
• White test

JEL CLASSIFICATION:

• C01
• C10

Acknowledgments

The authors thank the reviewers for their comments and suggestions which substantially improved the quality of the manuscript. The authors wish to thank Bent Nielsen and Christophe Croux for stimulating discussions and helpful comments.