# 29307

Автор(ов):

1

Параметры публикации
Тип публикации:
Пленарный доклад
Название:
Clusters of extreme values: models and estimation
ISBN/ISSN:
978-609-433-220-3
Наименование конференции:
11th International Vilnius Conference on Probability and Mathematical Statistics (Вильнюс, 2014)
Наименование источника:
Proceedings of the 11th International Vilnius Conference on Probability and Mathematical Statistics (Vilnius, 2014)
Город:
Вильнюс
Издательство:
TEV Publishers
Год издания:
2014
Страницы:
182
Аннотация
The interest to extremes in time series arisen as clusters of exceedances over a threshold is growing due to numerous applications in climate research, finance, telecommunications and social systems. Such clusters of exceedances are caused by dependence in time series. We define the cluster as a conglomerate containing consecutive exceedances of the underlying process $\{R_n\}$ over the threshold $u$ separated by return intervals with consecutive non-exceedances. We discuss geometric-like limit distributions of the cluster size %$T_2(x_{\rho_n})$ and inter-cluster size obtained in \cite{Markovich-a} under specific mixing condition based on such one used in \cite{Ferro}. The sequence of high $(1-\rho_n)$-order quantiles $x_{\rho_n}$ of the $\{R_n\}$ is used as the thresholds. The obtained distributions differ from the geometric distributions by the extremal index of the process $\{R_n\}$. The asymptotic first moments of both cluster characteristics are obtained \cite{Markovich-a}, \cite{Markovich-b}. Similarly, the result can be extended to moments of higher orders. In \cite{Markovich-a} the duration of clusters is defined as a sum of the random number of the weakly dependent regularly varying inter-arrival times between events of interest with tail index \$0
Библиографическая ссылка:
Маркович Н.М. Clusters of extreme values: models and estimation / Proceedings of the 11th International Vilnius Conference on Probability and Mathematical Statistics (Vilnius, 2014). Вильнюс: TEV Publishers, 2014. С. 182.