Publicação
Estimating the extremal index through local dependence
| Resumo: | The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition D(k)(un). We compare a process satisfying one of this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the D(2)(un) condition. We also analyze local dependence within moving maxima processes and derive a necessary and sufficient condition for D(k)(un). In order to evaluate the performance of the proposed estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a simulation study and compare with existing methods. An application to a financial time series is also presented. |
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| Autores principais: | Ferreira, Helena |
| Outros Autores: | Ferreira, Marta Susana |
| Assunto: | Extreme value theory Stationary sequences Dependence conditions Extremal index |
| Ano: | 2018 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition D(k)(un). We compare a process satisfying one of this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the D(2)(un) condition. We also analyze local dependence within moving maxima processes and derive a necessary and sufficient condition for D(k)(un). In order to evaluate the performance of the proposed estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a simulation study and compare with existing methods. An application to a financial time series is also presented. |
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