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

合作研究：通过样本分割对多元和函数时间序列进行统计推断

基本信息

批准号：
2210002
负责人：
Xiaofeng Shao
金额：
$ 20万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210002&HistoricalAwards=false
关键词：
Collaborative Research Statistical Inference Multivariate

项目摘要

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.

多变量和功能时间序列是普遍的，并且在许多领域都经常收集。这种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，并且在许多科学领域都有广泛的应用，包括生物信息学，商业，气候科学，经济学，金融，遗传学和信号处理。与现有方法相比，该研究项目将提供非参数推理程序，这些程序可以适应广泛的维度，并且需要对数据生成过程的假设较弱。该项目随之而来的方法将通过出版物，会议和研讨会演讲以及开源软件的开发传播到相关的科学社区。该项目将涉及多个研究指导计划，包括在扩大参与方面的努力，并将提供高级主题课程，以介绍时间序列分析中最先进的技术。该项目将在所有教育水平上提供广泛的跨学科培训机会，并将为未来的劳动力专业发展做出贡献。该项目将开发系统的方法和理论，内容涉及基于样本跨度（SS）和自我分类（SN）的多变量（包括高维）时间序列和功能时间序列的推断。最近，SN技术已推进了高维时间序列的推断，但需要使用修剪参数。同样，其适用性范围仅限于具有弱面板依赖性的高维时间序列，这在许多现代时间序列应用中可能是不现实的。反过来，现有的功能时间序列的SN依赖于功能主成分分析的尺寸缩小，因此，当替代方案与该过程中使用的顶级主要组件跨越的空间正交时，所得过程可能无能为力。为了解决这些主要局限性，该项目将开发一个基于SS-SN的新统一框架，并结合推断多变量和功能性时间序列的推断，并调查其在应用程序中的效用，以在低，中等，高或无限维度的时间序列中应用。该奖项通过评估企业的支持和众所周知的范围，反映了NSF的法定任务，并反映了构成的依据。