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Moment Bounds for Large Autocovariance Matrices Under Dependence

  • Fang HanEmail author
  • Yicheng Li
Article
  • 17 Downloads

Abstract

The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent data has been well understood, much less is known in the case of dependent data. We make a step toward filling this gap and establish deviation bounds that depend only on the parameters controlling the “intrinsic dimension” of the data up to some logarithmic terms. Our results have immediate impacts on high-dimensional time-series analysis, and we apply them to high-dimensional linear VAR(d) model, vector-valued ARCH model, and a model used in Banna et al. (Random Matrices Theory Appl 5(2):1650006, 2016).

Keywords

Autocovariance matrix Effective rank Weak dependence \(\tau \)-mixing 

Mathematics Subject Classification (2010)

60E15 60F10 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WashingtonSeattleUSA

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