Abstract #301039

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JSM 2003 Abstract #301039
Activity Number: 162
Type: Topic Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301039
Title: Extremal Co-Movements in Stock Markets: Characterization and Gamma Test
Author(s): Zhengjun Zhang*+
Companies: Washington University, St. Louis
Address: Department of Mathematics, St. Louis, MO, 63130,
Keywords: multivariate extremes ; extremal co-movements ; tail dependence index ; lag-$k$ tail dependence ; hypothesis testing ; financial risk
Abstract:

The drawbacks of the widely used Gumbel-type copulas are discovered by using simulation examples in modeling the tail dependencies of multiple time series. A new characterization of the asymptotic tail dependence index between two random variables is developed in this paper. Based on this new characterization, a test statistic, which we call it Gamma test (statistic), is proposed. This Gamma test effectively detects the asymptotic independencies or asymptotic dependencies of all simulation examples and provides insightful findings of real data of stock returns. This Gamma test not only tests the asymptotic independencies or dependencies between random variables within a random vector, but also tests lag-$k$ tail dependencies within each univariate sequence.

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