Nested Asymptotic (In)Dependent Extreme Value Copulas in Max-Stable Processes with Application to High-Frequency Financial Data

• Activity Number: 15
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Zhengjun Zhang*+ and Bin Zhu
• Companies: University of Wisconsin-Madison and University of Wisconsin
• Keywords: time series ; sparse multivariate maxima of moving maxima model ; GMM estimator ; finance

Abstract

Classical parametric max-stable processes are useful in describing asymptotic dependence from a probabilistic perspective, but their statistical applications are limited by infinite number of parameters in the processes, inflexibility of simultaneously modeling asymptotic independence and asymptotic dependence, rigid common marginal distributions, and hardly direct applicability to real data. This paper proposes a flexible model overcoming all of the aforementioned constraints. Two types of extreme value copulas are first nested in a class of asymptotically (in)dependent multivariate maxima and moving maxima (AIM4) processes with sparse random coefficients. The resulting model can now concurrently model asymptotic independence and/or asymptotic dependence within a group of random variables. After imposing a scale parameter and a shape parameter to each marginal variable, the final model can directly be applied to real data of intra-daily maxima of high-frequency financial time series. The paper presents probabilistic properties of the proposed model, statistical estimators and their properties, and illustrations with simulated data and real data.