• Corpus ID: 248266854

Statistics for Heteroscedastic Time Series Extremes

@inproceedings{Bucher2022StatisticsFH,
  title={Statistics for Heteroscedastic Time Series Extremes},
  author={Axel Bucher and Tobias Jennessen},
  year={2022}
}

• Axel Bucher, Tobias Jennessen
• Published 20 April 2022
• Mathematics

. Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31– 51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the observations are serially dependent, which is crucial for many practical applications. We prove a local limit theorem for a kernel estimator for the scedasis function, and a functional limit theorem for an estimator for the integrated scedasis function. We further prove consistency of a bootstrap scheme that allows to test for the null hypothesis that the extremes are homoscedastic. Finally, we propose an estimator for the extremal index governing the dynamics of the extremes and prove its consistency. All results are illustrated by Monte Carlo simulations. An important intermediate result concerns the sequential tail empirical process under serial dependence. Abstract. This supplementary material contains the remaining proofs for the main paper. Proofs for Sections 3-5 are presented in Sections A-C, respectively. Some auxiliary results are collected in Section D.