题目：Stationary vine copula models for multivariate time series

主讲人：Aleksey Min

时间：2025年5月29日  13:00

ZOOM会议：https://tum-conf.zoom.us/j/64438158134

     会议号: 644 3815 8134;密码: 318315

主持人：程宏

讲座简介：Copulas are multivariate distribution functions with uniformly distributed margins on the unit interval [0,1].Despite their simplicity, they are very helpful for modeling a dependence structure of multivariate data in applied science.  In the talk, I outline a flexible construction of copulas using graphical models vines.  Recently, the so-called vine copulas are successfully used to model univariate and multivariate time series. A time series consists of multiple observations indexed by time. Classical time series models allow for only linear dependence between variables and time points. Vine copulas can conveniently capture cross-sectional and temporal dependence of multivariate time series. In the talk, I derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition. I also discuss computationally efficient methods for estimation, simulation, and prediction.The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The talk is based on the joint work with Thomas Nagler and Daniel Krüger.

Copula是一类定义在单位区间[0,1]上、边缘分布均为均匀分布的多元分布函数。虽然其数学结构简洁，但在应用科学中，Copula在建模多元数据依赖结构方面具有重要作用和广泛应用。近年来，基于图模型的vine copula构造方法（藤图Copula）已成为建模单变量与多变量时间序列的有效工具。时间序列由按时间顺序排列的多个观测值组成，而传统的时间序列模型通常仅能捕捉变量间及时间点间的线性依赖关系，存在一定局限性。相比之下，vine copula能够灵活、便捷地刻画多元时间序列中的横截面依赖与时间依赖。本次讲座将系统介绍vine copula的灵活构造方法，推导在自然且可验证条件下能够保证时间序列平稳性的一类最大化图结构，并进一步讨论在估计、模拟与预测等方面的计算高效算法。该理论成果不仅允许模型设定存在一定偏差（misspecification），即使专门应用于独立同分布（iid）的情形，也能拓展现有文献的研究边界。讲座内容基于与Thomas Nagler和Daniel Krüger教授的合作研究成果，力求为多元依赖结构建模及其在时间序列分析中的应用提供新的理论视角与方法工具。

专家简介：Aleksey Min studied Mathematics at the Tashkent State University (Uzbekistan). In June 2004 he completed his Ph.D. on limit theorems for statistical functionals under supervision of Prof. Denker at the University of Göttingen. Since July 2004 he is a research associate at the Technical University of Munich. Aleksey Min first worked at the chair of Mathematical Statistics until March 2010. In April 2010 he changed to the chair of Mathematical Finance and became an academic advisor for students of the M.Sc. program Mathematical Finance and Actuarial Science. In January 2011 he habilitated at the Faculty of Mathematics of the TU München. Mr. Min was appointed as an adjunct professor by the TU Munich in February 2022..

阿列克谢·明在塔什干国立大学（乌兹别克斯坦）学习数学。2004年6月，他在哥廷根大学迪恩克教授的指导下完成了关于统计泛函极限定理的博士学位。自2004年7月起，他一直在慕尼黑工业大学担任研究助理。阿列克谢·明最初在数学统计学系工作，直至2010年3月。2010年4月，他转至数学金融系，并成为数学金融与精算科学硕士课程学生的学术顾问。2011年1月，他在慕尼黑工业大学数学系获得教授资格。2022年2月，明先生被慕尼黑工业大学任命为兼职教授。

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