Asymptotic expansions for blocks estimators: PoT framework

2023/09/06 by Zaoli Chen, Chen, Zaoli, Rafał Kulik +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2309.03163

openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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