A new blocks estimator for the extremal index

Abstract

The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal index is a recurrent theme in the literature and there are several methodologies for this purpose. The majority of existing methods depend on two parameters whose choice affects the performance of the estimators. Here we consider a new estimator depending only on one of the parameters, thus contributing to a decrease in the degree of uncertainty. A simulation study presents motivating results. An application to financial data will also be presented.

Keywords:

• Extreme value theory
• stationary sequences
• tail dependence
• extremal index

AMS 2000 SUBJECT CLASSIFICATION:

• Primary: 60G70
• Secondary: 62G32

Acknowledgements

The authors are very grateful to the referees for the comments, suggestions and corrections that contributed to the improvement of this work.

Additional information

Funding

The first author was partially supported by the research unit Center of Mathematics and Applications of University of Beira Interior UIDB/00212/2020 - FCT (Fundação para a Ciência e a Tecnologia). The second author was financed by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia within the Projects UIDB/00013/2020 and UIDP/00013/2020 of Center of Mathematics of the University of Minho, UIDB/00006/2020 and UIDP/00006/2020 of Center of Statistics and its Applications of University of Lisbon, UIDB/04621/2020 and UIDP/04621/2020 of Center for Computational and Stochastic Mathematics and PTDC/MAT-STA/28243/2017.