Discussion on paper ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’ by Zhengjun Zhang

Abstract

I would like to take this opportunity to congratulate Zhengjun for his continuing contribution to extremevalue statistics in recent years. In this review paper, some fundamental theories on univariate extremes and multivariate extremes are introduced, and recent developments on extremes from some structured stochastic processes are also given. The results in the latter sections of the paper are largely due to Zhengjun and his coauthors. The paper provides some insights for future challenges on extremes and can help young researchers follow the contemporary research topics. Below I offer some comments onunivariate extremevalue statistics. Although the theory for univariate extremes is quite complete, the statistical methods such as the estimation and inference procedures are far from perfect. Set μ = 0 and σ = 1 in the definition (2.6) in the paper and write