Using Triples to Assess Symmetry Under Weak Dependence

Abstract

The problem of assessing symmetry about an unspecified center of the one-dimensional marginal distribution of a strictly stationary random process is considered. A well-known U-statistic based on data triples is used to detect deviations from symmetry, allowing the underlying process to satisfy suitable mixing or near-epoch dependence conditions. We suggest using subsampling for inference on the target parameter, establish the asymptotic validity of the method in our setting, and discuss data-driven rules for selecting the size of subsamples. The small-sample properties of the proposed inferential procedures are examined by means of Monte Carlo simulations. Applications to time series of output growth and stock returns are also presented.

Keywords:

• Mixing
• Near-epoch dependence
• Subsampling
• Symmetry
• U-statistic

Acknowledgments

The authors are grateful to the associate editor and two referees for their helpful comments on an earlier version of this article.