Abstract Testing symmetry or quantile assumptions on the innovations distribution can be of invaluable help to improve or simplify the statistical procedures designed for GARCH-type models. In particular, evaluation of the conditional value-at-risk (VaR) or construction of confidence intervals for predictions requires estimating quantiles of the innovations distribution. We propose tests of different hypotheses: adequacy of a set of parametric quantiles, mean–median equality, symmetry of extreme quantiles, and zero-median in presence of a conditional mean. The tests rely on the asymptotic distribution of the empirical distribution function of the residuals. They are generally model-free (though not estimation-free) and thus are simple to implement. Efficiency comparisons are made using the Bahadur approach. Numerical studies based on simulated and real data are provided to illustrate the usefulness of the proposed tests for risk management or statistical purposes.

中文翻译：

---

检验半参数条件波动率模型中创新分布的假设

摘要 检验创新分布的对称性或分位数假设对于改进或简化为 GARCH 型模型设计的统计程序提供了宝贵的帮助。特别是，评估条件风险价值 (VaR) 或构建预测的置信区间需要估计创新分布的分位数。我们建议对不同假设进行检验：一组参数分位数的充分性、均值-中位数相等、极端分位数的对称性以及存在条件均值的零中位数。检验依赖于残差的经验分布函数的渐近分布。它们通常是无模型的（尽管不是无估计的），因此很容易实现。使用 Bahadur 方法进行效率比较。