Open Access
February 2012 Covariance matrix estimation for stationary time series
Han Xiao, Wei Biao Wu
Ann. Statist. 40(1): 466-493 (February 2012). DOI: 10.1214/11-AOS967


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.


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Han Xiao. Wei Biao Wu. "Covariance matrix estimation for stationary time series." Ann. Statist. 40 (1) 466 - 493, February 2012.


Published: February 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1246.62191
MathSciNet: MR3014314
Digital Object Identifier: 10.1214/11-AOS967

Primary: 62M10
Secondary: 62H12

Keywords: Autocovariance matrix , banding , large deviation , physical dependence measure , short range dependence , Spectral density , stationary process , tapering , thresholding , Toeplitz matrix

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
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