Discussion on “on studying extreme values and systematic risks with nonlinear time series models and tail dependence measures”

Extreme value theory provides essential mathematical foundations for modelling tail risks and has wide applications. The emerging of big and heterogeneous data calls for the development of new extreme value theory and methods. For studying high-dimensional extremes and extreme clusters in time series, an important problem is how to measure and test for tail dependence between random variables. Section 3.1 of Dr. Zhang’s paper discusses some newly proposed tail dependence measures. In the era of big data, a timely and challenging question is how to study data from heterogeneous populations, e.g. from different sources. Section 3.2 reviews some new developments of extreme value theory for maxima of maxima. The theory and methods in Sections 3.1 and 2.3 set the foundations for modelling extremes of multivariate and heterogeneous data, and we believe they have wide applicability. We will discuss two possible directions: (1) measuring and testing of partial tail dependence; (2) application of the extreme value theory for maxima of maxima in highdimensional inference.