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Asymptotic expansions for blocks estimators: PoT framework

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  • Chen, Zaoli
  • Kulik, Rafał

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.

Suggested Citation

  • Chen, Zaoli & Kulik, Rafał, 2026. "Asymptotic expansions for blocks estimators: PoT framework," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925001875
    DOI: 10.1016/j.spa.2025.104744
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    References listed on IDEAS

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    1. Bucher, Axel & Segers, Johan, 2018. "Inference for heavy tailed stationary time series based on sliding blocks," LIDAM Reprints ISBA 2018007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    4. Hsing, Tailen, 1991. "Estimating the parameters of rare events," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 117-139, February.
    5. Zhengyan Lin & Zhidong Bai, 2010. "Elementary Inequalities of Probabilities of Events," Springer Books, in: Probability Inequalities, chapter 0, pages 1-8, Springer.
    6. Buriticá, Gloria & Mikosch, Thomas & Wintenberger, Olivier, 2023. "Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 68-101.
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