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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>-mixing, while asymptotic normality follows from <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>-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.</p>

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Conditional extreme value estimation for dependent time series

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Martin Bladt,
  • Laurits Glargaard,
  • Theodor Henningsen

摘要

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 \(\alpha\) -mixing, while asymptotic normality follows from \(\beta\) -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.