Conditional Extreme Value Estimation for Dependent Time Series

Fuente: arXiv
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Autori principali: Bladt, Martin, Glargaard, Laurits, Henningsen, Theodor
Natura: Preprint
Pubblicazione: 2025
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author Bladt, Martin
Glargaard, Laurits
Henningsen, Theodor
author_facet Bladt, Martin
Glargaard, Laurits
Henningsen, Theodor
contents We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established under $α$-mixing, while asymptotic normality follows from $β$-mixing and second-order conditions. A key aspect of our approach is its versatile functional formulation in terms of the conditional tail process. Simulations demonstrate its performance across dependence scenarios. We apply our method to extreme event modelling in the oil industry, revealing distinct tail behaviours under varying conditioning values.
format Preprint
id arxiv_https___arxiv_org_abs_2503_22366
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Conditional Extreme Value Estimation for Dependent Time Series
Bladt, Martin
Glargaard, Laurits
Henningsen, Theodor
Statistics Theory
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established under $α$-mixing, while asymptotic normality follows from $β$-mixing and second-order conditions. A key aspect of our approach is its versatile functional formulation in terms of the conditional tail process. Simulations demonstrate its performance across dependence scenarios. We apply our method to extreme event modelling in the oil industry, revealing distinct tail behaviours under varying conditioning values.
title Conditional Extreme Value Estimation for Dependent Time Series
topic Statistics Theory
url https://arxiv.org/abs/2503.22366