Moment Bounds for Large Autocovariance Matrices Under Dependence

Fang Han () and Yicheng Li ()
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Fang Han: University of Washington
Yicheng Li: University of Washington

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1445-1492

Abstract: 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; $$\tau $$ τ -mixing; 60E15; 60F10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-019-00922-z

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