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December 2013 Covariance and precision matrix estimation for high-dimensional time series
Xiaohui Chen, Mengyu Xu, Wei Biao Wu
Ann. Statist. 41(6): 2994-3021 (December 2013). DOI: 10.1214/13-AOS1182


We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150–14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate of convergence. Asymptotic properties are also obtained for the precision matrix estimate which is based on the graphical Lasso principle. Our theory substantially generalizes earlier ones by allowing dependence, by allowing nonstationarity and by relaxing the associated moment conditions.


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Xiaohui Chen. Mengyu Xu. Wei Biao Wu. "Covariance and precision matrix estimation for high-dimensional time series." Ann. Statist. 41 (6) 2994 - 3021, December 2013.


Published: December 2013
First available in Project Euclid: 1 January 2014

zbMATH: 1294.62123
MathSciNet: MR3161455
Digital Object Identifier: 10.1214/13-AOS1182

Primary: 62H12
Secondary: 62M10

Keywords: consistency , Covariance matrix , Dependence , functional dependence measure , high-dimensional inference , Lasso , Nagaev inequality , nonstationary time series , precision matrix , Sparsity , spatial–temporal processes , thresholding

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • December 2013
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