AI 中文总结
针对重尾长记忆线性时间序列的序列尾部相依估计量，提出两种新型多元归约原理，证明其中心极限定理，发现长记忆设定下与短程相依结果存在显著差异，解决了经验极值图的相关理论问题。
AI 中文摘要
我们证明了重尾长记忆线性时间序列中序列尾部相依估计量的多个中心极限定理。主要理论工具是针对重尾长记忆线性时间序列部分和的两种新型多元归约原理，这些原理基于滑动窗口及随样本量增长的阈值进行从属。这需要解决若干重大困难，包括处理非线性、依赖样本量的多元从属机制、多个重叠线性过程之间的相依性，以及边际分布高阶矩的缺失。尽管存在这些障碍，我们的假设较为温和，尤其允许创新过程具有无限方差。我们理论的一个关键特征是第二种归约原理在阈值上一致成立，这使得以样本分位数作为阈值的经验极值图的中心极限定理得以成立。尽管带随机阈值的经验极值图版本在实践中无处不在，但该问题在序列极值相依估计的文献中受到的关注很少。我们在多个方面将我们的结果与短程相依下可能得到的结果进行比较，从而发现在我们的长记忆设定中收敛速度和极限定律存在显著差异。
英文摘要
We prove multiple central limit theorems for serial tail dependence estimators in heavy-tailed long memory linear time series. The main theoretical tools are two novel multivariate reduction principles for partial sums of heavy-tailed long memory linear time series, subordinated over sliding windows and above a threshold growing with sample size. This requires addressing several substantial difficulties, including handling a nonlinear, sample-size dependent, and multivariate subordination mechanism, the dependence between several overlapping linear processes, and the lack of higher-order moments of the marginal distribution. Despite these obstacles, our assumptions are mild and, in particular, the innovation process is allowed to have infinite variance. A key feature of our theory is that our second reduction principle holds uniformly in the threshold, allowing central limit theory for empirical extremograms with sample quantiles as thresholds. This question has received little attention in the literature on serial extremal dependence estimation even though the version of empirical extremograms with random thresholds is ubiquitous in practice. We compare our results in several respects with those that may be obtained under short-range dependence, thereby discovering markedly different convergence rates and limit laws in our long memory setting.
Comments87 pages
