Covariance and precision matrix estimation for high-dimensional time series

Xiaohui Chen; Mengyu Xu; Wei Biao Wu

doi:10.1214/13-aos1182

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arXiv · 1401.0993

Covariance and precision matrix estimation for high-dimensional time series

Xiaohui Chen·Mengyu Xu·Wei Biao Wu

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Abstract

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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BibTeX RIS

Xiaohui Chen, Mengyu Xu, Wei Biao Wu. 2014-01-06. Covariance and precision matrix estimation for high-dimensional time series. https://doi.org/10.1214/13-aos1182

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