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.
