Abstract 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.

中文翻译：

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对称性测试与 iid 和非 iid 设置中的一些偏对称替代方案的比较

摘要 根据经验功效与一些灵活的偏斜对称替代方案，对一系列近期和经典的对称性检验进行了比较。比较是针对 iid 数据以及线性和 GARCH 时间序列模型进行的。此外，还对测试进行了计算效率分析。指出了无分布测试的作用，它避免了用于确定经验功效和 p 值的耗时重采样技术。针对一类无分布检验讨论了 iid 和 GARCH 模型中检验统计量的渐近等价。