Collaborative Research: Statistical Inference for Multivariate and Functional Time Series via Sample Splitting

多变量时间序列和函数时间序列在许多领域中普遍存在，并被常规收集。这类时间序列的统计推断是现代时间序列分析中的一个基本问题，在生物信息学、商业、气候科学、经济、金融、遗传学和信号处理等科学领域有着广泛的应用。与现有的方法相比，本研究项目将提供非参数推理程序，可以适应广泛的维度范围，并且对数据生成过程的假设较弱。该项目所采用的方法将通过出版物、会议和研讨会介绍以及开放源码软件的开发向相关科学界传播。该项目将涉及多项研究指导举措，包括努力扩大参与，并将提供高级专题课程，介绍时间序列分析中的最新技术。该项目将在所有教育水平提供广泛的跨学科培训机会，并将有助于未来劳动力的专业发展。该项目将发展一套系统的方法和理论，用于基于样本分裂(SS)和自我归一化(SN)的多变量(包括高维)时间序列和函数时间序列的推断。最近，SN技术已经发展到高维时间序列的推断，但它需要使用一个修剪参数。此外，它的适用范围仅限于具有弱面板相关性的高维时间序列，这在许多现代时间序列应用中可能是不现实的。反过来，现有的函数时间序列的SN依赖于通过函数主成分分析进行的降维，因此，当备选方案与该过程中使用的顶主成分所跨越的空间正交时，所得到的过程可能是无效的。为了解决这些主要限制，该项目将开发一个基于SS-SN的新的统一框架，结合对多变量和函数时间序列的推断，并调查其在低、中、高或无限维时间序列分析中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Multivariate and functional time series are prevalent and routinely collected in many fields. Statistical inference of such time series is a fundamental problem in modern time series analysis and has broad applications in many scientific areas, including bioinformatics, business, climate science, economics, finance, genetics, and signal processing. Compared with existing methodologies, this research project will provide nonparametric inference procedures that can accommodate a wide range of dimensionality and require weak assumptions on the data generating processes. The methodology ensuing from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations, and the development of open-source software. The project will involve multiple research mentoring initiatives, including efforts on broadening participation, and will offer advanced topic courses to introduce the state-of-the-art techniques in time series analysis. The project will provide a broad range of interdisciplinary training opportunities at all educational levels and will contribute to the future workforce professional development.The project will develop a systematic body of methods and theory on inference for both multivariate (including high-dimensional) time series and functional time series based on sample splitting (SS) and self-normalization (SN). Recently, the SN technique has been advanced to the inference of high-dimensional time series, but it requires the use of a trimming parameter. Also, its scope of applicability is limited to high-dimensional time series with weak panel dependence which might be unrealistic in many modern time series applications. In turn, the existing SN for functional time series relies on dimension reduction by functional principal component analysis and, hence, the resulting procedure may be powerless when the alternative is orthogonal to the space spanned by the top principal components used in the procedure. To address these major limitations, this project will develop a new unified framework based on SS-SN, in conjunction with inference for multivariate and functional time series, and investigate its utility in application to analysis of time series of low, medium, high or infinite dimensions.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.