Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting

A wide set of recent and classical symmetry tests is compared in terms of empirical power against some flexible skew-symmetric alternatives. The comparison is done for i.i.d. data, as well as for linear and GARCH time series models. In addition, the tests are analyzed in terms of computational efficiency. The role of distribution-free tests that avoid time-consuming resampling techniques for determining empirical powers and p-values is pointed out. An asymptotic equivalence of test statistics in the i.i.d. and GARCH models is discussed for a class of distribution-free tests.