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.

该项目的目的是建立一个系统的渐近理论，以估计时间序列中的大维协方差矩阵；高维推断中的基本问题。特别是，研究人员计划研究样品协方差和样品协方差矩阵的固定过程的特性；处理固定过程的协方差矩阵及其在预测和其他问题中的应用；并通过估计高阶累积量量来探索随机过程的非高斯特征。协调矩阵在包括环境科学，工程，经济学和金融等各个领域中起着基本作用。在分析，测试，监测和预测地震，经济和金融以及其他时间序列时，需要估算协方差矩阵。该项目开发的结果可以为估计协方差矩阵提供理论基础，并有可能改善用于各种应用中使用的时间序列处理算法。