Sparse-Moving Maxima Models for Extreme Dependence in Multivariate Financial Time Series

• Activity Number: 107
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Zhengjun Zhang*+
• Companies: University of Wisconsin
• Keywords: Extreme value theory ; GMM estimator ; Value-at-Risk ; Max-stable processes

Abstract

The multivariate maxima of moving maxima (M4) model has the potential to model both the cross-sectional and temporal tail-dependence for a rich class of multivariate time series. The main difficulty of applying M4 model to real data is due to the estimation of a large number of parameters in the model and the intractability of its joint likelihood. In this paper, we consider a sparse M4 random coefficient model (SM4R), which has a parsimonious number of parameters and it can adequately capture all the major stylized facts exhibited by financial time series found in recent empirical studies. We study the probabilistic properties of the newly proposed model and develop a new approach for statistical inference based on the generalized method of moment (GMM). We also demonstrate through real data analysis that the SM4R model can be effectively used to improve the estimates of the value at risk for portfolios consisting of multivariate financial returns while ignoring either temporal or cross-sectional extreme dependence could result in serious underestimate of market risk.