Covariance Matrix Estimation in Time Series and Its Applications

时间序列中的协方差矩阵估计及其应用

• 批准号: 1106790
• 负责人: Wei Biao Wu
• 金额: $ 27.69万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106790&HistoricalAwards=false
• 关键词: Covariance; Matrix; Estimation; Time; Series

The goal of this project is to establish a systematic asymptotic theory for estimates of large dimensional covariance matrices in time series; a fundamental problem in high-dimensional inference. In particular, the investigator plans to study properties of sample covariances and sample covariance matrices for stationary processes; deal with consistent estimation of covariance matrices of stationary processes and its applications in prediction and other problems; and explore non-Gaussian features of random processes by estimating higher order cumulant tensors.Covariance matrices play a fundamental role in various fields including environmental science, engineering, economics and finance. Estimation of covariance matrices is needed in analyzing, testing, monitoring and predicting of seismic, economic and financial and other time series. Results developed from this project can provide a theoretical foundation for estimation of covariance matrices and can potentially improve time series processing algorithms that are used in various applications.

本课题的目标是建立一个系统的渐近理论估计的大维协方差矩阵的时间序列；高维推理中的一个基本问题。特别是，研究者计划研究平稳过程的样本协方差和样本协方差矩阵的性质；处理平稳过程协方差矩阵的一致估计及其在预测中的应用等问题；并通过估计高阶累积张量来探索随机过程的非高斯特征。协方差矩阵在环境科学、工程、经济和金融等领域发挥着重要作用。在地震、经济、金融等时间序列的分析、检验、监测和预测中都需要协方差矩阵的估计。从这个项目中发展出来的结果可以为协方差矩阵的估计提供理论基础，并且可以潜在地改进在各种应用中使用的时间序列处理算法。