COVARIANCE MATRIX ESTIMATION FOR STATIONARY TIME SERIES

被引：64

作者：

Xia, Han ^{[1
]}

Wu, Wei Biao ^{[1
]}

机构：

[1] Univ Chicago, Dept Stat, Chicago, IL 60637 USA

来源：

ANNALS OF STATISTICS | 2012年 / 40卷 / 01期

基金：

美国国家科学基金会;

关键词：

Autocovariance matrix; banding; large deviation; physical dependence measure; short range dependence; spectral density; stationary process; tapering; thresholding; Toeplitz matrix; CENTRAL-LIMIT-THEOREM; LARGE DEVIATIONS; QUADRATIC-FORMS; LARGEST EIGENVALUE; AUTOCOVARIANCE MATRICES; MODERATE DEVIATIONS; GAUSSIAN-PROCESSES; RANDOM-VARIABLES; PERIODOGRAM; MAXIMUM;

D O I：

10.1214/11-AOS967

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms of the covariances. We develop a large deviation result for quadratic forms of stationary processes using m-dependence approximation, under the framework of causal representation and physical dependence measures.

引用

页码：466 / 493

页数：28