We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from internal clusters and boundary clusters. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between small blocks and large blocks scenario.

翻译：本文考虑在超阈值（Peak-over-Threshold, PoT）框架下，针对多元正则变化时间序列的聚类指数，采用非重叠块估计量与滑动块估计量。我们旨在完整描述这些估计量的极限行为。通过对滑动块统计量与非重叠块统计量之差进行精确展开，我们实现了这一目标。该展开的速率源自内部聚类与边界聚类。为获取这些速率，我们需要扩展现有关于聚类测度模糊收敛的结果。我们揭示了小块与大块情景之间的二分行为。