CAREER: Statistical Inference of Tail Dependent Time Series

该项目旨在为尾部相依时间序列分析开发一种新的理论框架和统计推断方法，并就其理论和实践对未来的统计学家和数据科学家进行教育。尾部相依时间序列作为一种新兴的数据类型，在精算、气候科学、经济、金融、水文学、互联网流量工程等领域得到了广泛的观察和认可。理解并适当适应尾部依赖现象的任务对于地震、飓风和金融危机等极端事件的建模非常重要。该项目的成果将在气候科学、经济学、精算科学、金融、水文学和互联网交通工程等科学领域产生重大影响。该提案还涉及一项综合教育计划，让本科生和高中生接触这个主题，让研究生和高级本科生具备分析尾部相依时间序列所需的统计推理和分析技能，并指导博士生成为该领域教育和研究的未来领导者。现有的研究尾部相依时间序列的方法往往依赖于某些参数模型来描述潜在的尾部相依结构。这特别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类一般的尾部相依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根本问题。使用新提出的框架，该项目将向尾部m相关近似格式发展有意义的结果，该方案可用作获得尾部相关数据统计的极限定理的有力工具。与传统的m相关近似相比，当前的设置可能更具挑战性，因为存在双重渐近性，即随着样本量的增加，分位数指数被允许接近于零或一，以反映极端风险。该项目将研究几个尾部相依时间序列的统计推断问题，包括高分位数估计及其相关可信区间的构造，尾部相依可视化和检验，极值理论对极高分位数的推断，高和极高分位数回归模型的扩展，以及高维非平稳设置。有待开发的结果有望有助于识别某些气候科学和经济数据中未发现的特征，并适用于其他涉及尾部相关时间序列分析的科学问题。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.