Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the observations are serially dependent, which is crucial for many practical applications. We prove a local limit theorem for a kernel estimator for the scedasis function, and a functional limit theorem for an estimator for the integrated scedasis function. We further prove consistency of a bootstrap scheme that allows to test for the null hypothesis that the extremes are homoscedastic. Finally, we propose an estimator for the extremal index governing the dynamics of the extremes and prove its consistency. All results are illustrated by Monte Carlo simulations. An important intermediate result concerns the sequential tail empirical process under serial dependence.

翻译：Einmahl、de Haan和Zhou(2016年,《皇家统计学会期刊》:系列B、78(1)、31-51)最近引入了一个允许极端异性性化的随机模型,该模型扩展至观测具有连续依赖性的情况,这对许多实际应用至关重要。我们证明,对于一个内核测深线函数的测深器来说,我们有一个局部的限值,对于一个综合拼贴功能的测深器来说,一个功能性限值。我们进一步证明,一个靴套计划是一致的,能够测试极端是同质性的无效假设。最后,我们提议了一个极端动态极端指数的估测值,以证明其一致性。所有结果都由蒙特卡洛模拟加以说明。一个重要的中间结果涉及序列依赖下的连续尾巴经验过程。