CAREER: Statistical Inference of Tail Dependent Time Series

该项目旨在为尾相关时间序列的分析开发新的理论框架和统计推断方法，并为未来的统计学家和数据科学家提供理论和实践方面的教育。尾相关时间序列作为一种新兴的数据类型，已经在精算科学、气候科学、经济、金融、水文学、互联网流量工程等多个领域得到了观察和认可。理解和适当适应尾部依赖现象的任务对于极端事件（如地震、飓风和金融危机）的建模具有重要意义。该项目的成果将对气候科学、经济学、精算科学、金融、水文学和互联网流量工程等科学领域产生重大影响。该提案还包括一个综合教育计划，让本科生和高中生接触到这个主题，让研究生和高级本科生具备分析尾相关时间序列的统计推理和分析技能的理想水平，并指导博士生成为该领域教育和研究的未来领导者。研究尾相关时间序列的现有方法往往依赖于某些参数模型来描述潜在的尾相关结构。这主要是由于缺乏一个方便和严格的框架，人们可以使用它来获得一般类型的尾相关时间序列所需的极限定理。该项目旨在通过提出一个基于因果表示和对抗性尾部耦合技术的新框架来解决这一基本问题。使用新提出的框架，该项目将对尾m相关近似方案开发有意义的结果，然后可以用作获得尾相关数据统计极限定理的强大工具。与传统的依赖于m的近似相比，由于双渐近性，当前的设置可能更具挑战性，其中分位数指数可以随着样本量的增加而接近零或1，以反映极端风险。本项目将研究尾相关时间序列的几个统计推断问题，包括高分位数估计及其相关置信区间构建、尾相关可视化和测试、使用极值理论推断极高分位数、扩展到高和极高分位数回归模型以及高维非平稳设置。待开发的结果预计将有助于确定某些气候科学和经济数据中未被发现的特征，并适用于涉及尾相关时间序列分析的其他科学问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project aims to develop a new theoretical framework and statistical inference methods for the analysis of tail dependent time series, and to educate future statisticians and data scientists on its theory and practice. Tail dependent time series, as an emerging data type, has been observed and recognized in various fields including actuarial science, climate science, economics, finance, hydrology, and internet traffic engineering, among others. The task of understanding and appropriately accommodating the phenomenon of tail dependence can be of significant importance to the modeling of extreme events such as earthquakes, hurricanes, and financial crises. The results from the project will make significant impacts in scientific areas such as climate science, economics, actuarial science, finance, hydrology and internet traffic engineering. The proposal also involves an integrated education plan to expose undergraduate and high school students to the topic, to equip graduate and advanced undergraduate students with a desirable level of statistical reasoning and analytical skills for analyzing tail dependent time series, and to mentor doctoral students to become future leaders in the education and research of the area. Existing methods for studying tail dependent time series often rely on certain parametric models for describing the underlying tail dependence structure. This is particularly due to the lack of a convenient and rigorous framework that one can use to obtain desired limit theorems for a general class of tail dependent time series. The project aims to address this fundamental problem by proposing a new framework based on the causal representation and the technique of adversarial tail coupling. Using the newly proposed framework, the project will develop meaningful results toward a tail m-dependent approximation scheme, which can then be used as a powerful tool to obtain limit theorems for statistics of tail dependent data. Compared with the conventional m-dependent approximation, the current setting can be more challenging due to the double asymptotics where the quantile index is allowed to approach either zero or one as the sample size increases to reflect extreme risks. The project will study several statistical inference problems for tail dependent time series, including high quantile estimation and its associated confidence interval construction, tail dependence visualization and testing, inference of extremely high quantiles using the extreme value theory, extensions to high and extremely high quantile regression models, and high-dimensional nonstationary settings. The results to be developed are expected to be useful in identifying undiscovered features in certain climate science and economic data, and applicable to other scientific problems that involve the analysis of tail dependent time series.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.