学术报告一

报告题目: Extremogram, cross-extremogram, and ex-periodogram

报告人：Thomas Mikosch (University of Copenhagen)

报告时间；2018年5月31日上午9:00-11:00

报告地点：星际电子在线学术报告厅（25教14楼报告厅）

摘要: The extremogram is an analog of the autocorrelation function (ACF) for the extremes in a strictly stationary Rd-valued time series (Xt). It was introduced by Davis and Mikosch in 2008/2009. In contrast to the ACF which measures the degree of lag-wise linear dependence, the extremogram focuses on the lag-wise dependence of extreme events. An extreme event at time t happens when Xt falls into a set far away from the origin. In this context, it is convenient to assume that the underlying time series is regularly varying. This means that the _nite-dimensional distributions of the series are multivariate regularly varying. We will explain this notion and consider various examples such as regularly varying linear, GARCH, and stochastic volatility processes. We will provide limit theory for the sample extremogram and its Fourier analog, the ex-periodogram, and explain how these statistics can be used to detect extremal serial dependence in the series. Finally, we consider modi_cations like the cross-extremogram, an analog of the cross-correlation function of two time series, and the return extremogram.

报告人简介：Mikosch教授现任教于哥本哈根大学数学科学系;于1981年在德累斯顿(TU Dresden)获数学硕士学位;于1984年在圣彼得堡大学(St. Petersburg University)获得概率论博士学位;在2001年1月1日加入该系之前，他曾在德累斯顿、富士、惠灵顿、格罗宁根等地工作过。目前主要从事应用概率、渐近理论、时间序列分析、保险和金融数学、随机过程和极值理论等方向的研究。在很多高级期刊发表作品，成果颇丰。更多的介绍见其个人主页：http://www.math.ku.dk/~mikosch/

学术报告二

报告题目：Extreme value analysis without the largest values: what can be done?

报告人：Professor Gennady Samorodnitsky, Cornell University

报告时间；2018年5月31日上午9:00-11:00

报告地点：星际电子在线学术报告厅（25教14楼报告厅）

摘要： Motivated by an analysis of the degree distributions in a large social network, we are concerned with the analysis of heavy-tailed data when a portion of the extreme values are unavailable. We focus on the Hill estimator, which plays a starring role in heavy-tailed modeling. The Hill estimator for this data exhibited a smooth and increasing “sample path” as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation, we introduce a new parameterization into the Hill estimator that corresponds to the proportion of extreme values that are unavailable and the proportion of upper order statistics used normalized Hill estimator to a Gaussian random field. An estimation procedure is developed based on the limit theory to estimate the number of missing extremes and extreme value parameters including the tail index and the bias of Hill’s estimate. We illustrate how this approach works in both simulations and real data examples.

报告人简介：Gennady Samorodnitsky教授现任教于康奈尔(Cornell University)大学运筹学与信息工程系;在1978年于莫斯科钢和合金研究所（Moscow Steel and Alloys Institute, USSR）Gennady Samorodnitsky获学士学位；1978于苏联（Technion）获硕士学位；1986于以色列获博士学位。1988年加入运筹学与信息工程系。主要的研究领域是概率论及其应用，其中一个重要领域是随机建模，尤其是厚尾或相依长尾的“非标准”模型。同时，他也对交互的拓扑,几何和遍历理论的概率理论等十分感兴趣，在所研究专业已有丰硕的研究成果。具体可见其主页。