Randomization tests of copula symmetry

TL;DR

This paper introduces new nonparametric resampling-based tests for copula symmetry and exchangeability, effectively detecting asymmetries without needing margin information or tuning parameters.

Contribution

The paper proposes a novel resampling procedure exploiting group invariance for testing copula symmetry, improving upon existing methods in simplicity and performance.

Findings

Control size asymptotically

Consistently detect asymmetry

Perform well in small samples

Abstract

New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of margins. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared to existing procedures involving the multiplier bootstrap.