On the Estimation of the Extremal Index Based on Scaling and Resampling

Journal of Computational and Graphical Statistics, Vol. 18, No. 3, pp. 731-755, 2009

38 Pages Posted: 14 Apr 2010

See all articles by Kam Hamidieh

Kam Hamidieh

University of Pennsylvania; Statistics and Data Sciences

Stilian Stoev

Boston University - Department of Mathematics and Statistics

George Michailidis

University of Michigan at Ann Arbor

Date Written: April 14, 2009

Abstract

The extremal index parameter characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance, and environmental studies. In this study, a novel estimator for the extremal index based on the asymptotic scaling of block-maxima and resampling is introduced. It is shown to be consistent and asymptotically normal for a large class of m-dependent time series.

Further, a procedure for the automatic selection of its tuning parameter is developed and different types of confidence intervals that prove useful in practice proposed. The performance of the estimator is examined through simulations, which show its highly competitive behavior. Finally, the estimator is applied to three real datasets of daily crude oil prices, daily returns of the S&P 500 stock index, and high-frequency, intraday traded volumes of a stock. These applications demonstrate additional diagnostic features of statistical plots based on the new estimator.

Keywords: Extremal Index, Clustering, Asymptotic normality, Bootstrap, Heavy tails, Permutation

JEL Classification: C1

Suggested Citation

Hamidieh, Kamal and Stoev, Stilian and Michailidis, George, On the Estimation of the Extremal Index Based on Scaling and Resampling (April 14, 2009). Journal of Computational and Graphical Statistics, Vol. 18, No. 3, pp. 731-755, 2009 , Available at SSRN: https://ssrn.com/abstract=1589883

Kamal Hamidieh (Contact Author)

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

Statistics and Data Sciences ( email )

2317 Speedway
Austin, TX 78712
United States

Stilian Stoev

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

George Michailidis

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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