Collaborative Research: Asymptotic Statistical Inference for High-dimensional Time Series

合作研究：高维时间序列的渐近统计推断

• 批准号: 1916351
• 负责人: Wei Biao Wu
• 金额: $ 19万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916351&HistoricalAwards=false
• 关键词: Collaborative; Research; Asymptotic; Statistical; Inference

The information era has witnessed an explosion in the collection of high dimensional time series data across a wide range of areas, including finance, signal processing, neuroscience, meteorology, seismology, among others. For low dimensional time series, there is a well-developed estimation and inference theory. Inference theory in the high dimensional setting is of fundamental importance and has wide applications, but has been rarely studied. Researchers face a number of challenges in solving real-world problems: (i) complex dynamics of data generating systems, (ii) temporal and cross-sectional dependencies, (iii) high dimensionality and (iv) non-Gaussian distributions. The goal of this project is to develop and advance inference theory for high dimensional time series data by concerning all the above characteristics. The project will provide training to graduate students and publicly avaialble statistical packages. This project involves developing a systematic asymptotic theory for estimation and inference for high dimensional time series, including parameter estimation, construction of simultaneous confidence intervals, prediction, model selection, Granger causality test, hypothesis testing, and spectral domain estimation. To this end, a new methodology for the estimation of parameters and second-order characteristics for high dimensional time series will be proposed. New tools and concentration inequalities for the asymptotic analysis of high-dimensional time series will be developed. To perform simultaneous inference and significance testing, the PIs will investigate the very deep Gaussian approximation problem and the high dimensional central limit theorems by taking both high dimensionality and temporal and cross-sectional dependencies into account.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.

信息时代见证了金融、信号处理、神经科学、气象学、地震学等广泛领域高维时间序列数据收集的爆炸式增长。对于低维时间序列，有成熟的估计和推断理论。高维环境中的推理理论具有基础重要性并具有广泛的应用，但研究很少。研究人员在解决现实世界问题时面临着许多挑战：（i）数据生成系统的复杂动态，（ii）时间和横截面依赖性，（iii）高维性和（iv）非高斯分布。该项目的目标是通过考虑所有上述特征来开发和推进高维时间序列数据的推理理论。该项目将为研究生提供培训并提供公开的统计数据包。该项目涉及开发用于高维时间序列估计和推理的系统渐近理论，包括参数估计、同时置信区间的构建、预测、模型选择、格兰杰因果检验、假设检验和谱域估计。为此，将提出一种新的高维时间序列参数和二阶特征估计方法。将开发用于高维时间序列渐近分析的新工具和集中不等式。为了同时进行推理和显着性测试，PI 将通过考虑高维性以及时间和横截面依赖性来研究非常深的高斯近似问题和高维中心极限定理。该奖项反映了 NSF 的法定使命，并被视为值得通过使用基金会的智力优点和更广泛的影响审查标准进行评估来支持。