学术报告：A Sparse Max–Fréchet Framework for Multivariate Clustered Extremes with an Application to Cryptocurrency Spillovers

报告时间：10月28日（星期二）上午 9:00-10:00

报告地点：学院南路校区，主教 301

主持人：邓露 教授

报告人：张正军，中国科学院大学，教授

报告摘要：Multivariate extreme value analysis faces major challenges in high dimensions, particularly when both temporal persistence and cross-sectional dependence must be modeled. Classical approaches such as the multivariate maxima of moving maxima (M4) process are computationally intractable and produce unrealistic dependence patterns, while dynamic univariate models like the autoregressive conditional Fréchet (AcF) are limited by independence assumptions in innovations. We propose a unified econometric framework that addresses these limitations. First, we introduce a sparse variant of the M4 model (vSM4R), which provides a parsimonious factor structure for multivariate extremes. Second, we extend the AcF model to an m-dependent setting (mAcF), capturing clustered tail behavior across time. Third, we integrate these into a dynamic multivariate Fréchet framework (mAcF–vSM4R). We derive probabilistic properties and develop a composite likelihood estimator, establishing its consistency and asymptotic normality. Monte Carlo evidence supports strong finite-sample performance. An empirical illustration with cryptocurrency returns, a real-world application, shows the model’s ability to capture time-varying tail dependence and spillovers, providing empirical validation of our framework, while the main contribution is methodological.

报告人简介：张正军教授现为中国科学院大学经济与管理学院长聘教授和统计与数据科学系系主任，原美国威斯康辛大学统计系终身教授和系副主任，国际数理统计协会执行委员和财务总监（July 2016 -- July 2022），国际数理统计协会会士，美国统计协会会士。现担任JASA，JBES，Statistica Sinica，JDS，EJS等国际期刊副主编。主要研究方向包括计量经济学、金融计量学、计算医学与实践、 极端气候等等。在国际顶级期刊：统计（AoS，JASA，JRSSB）、计量（JoE, EE）、金融（JBES, JBF）、医学（AFM，Vaccines）、气象(ATM)等发表论文上百篇。代表性思想和作品包括商相关系数（QCC、TQCC）、非对称广义相关系数（GMC）、滞后尾部相依系数、最大线性回归、最大逻辑回归、EGB2期权定价公式、盯市在险价值（MMVaR）、条件极值Frechet自回归（AcF）等等。

撰稿人：刘洁

审稿人：邓露