论文标题
异性时间序列极端的统计数据
Statistics for Heteroscedastic Time Series Extremes
论文作者
论文摘要
Einmahl，de Haan和Zhou（2016年，皇家统计学会杂志：B系列，78（1），31-51）最近引入了一个随机模型，允许极端的异质性。该模型扩展到观察结果串行依赖的情况，这对于许多实际应用至关重要。我们证明了SCEDASIS函数内核估计器的局部限制定理，以及集成SCEDASIS函数的估计器的功能极限定理。我们进一步证明了引导程序方案的一致性，该方案允许检验零假设，即极端是同质的。最后，我们提出了一个管理极端动态的极端索引的估计量，并证明了它的一致性。所有结果均通过蒙特卡洛模拟说明。一个重要的中间结果涉及在串行依赖性下的顺序尾部经验过程。
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.
