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Moment Bounds for Large Autocovariance Matrices Under Dependence

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  • Fang Han

    (University of Washington)

  • Yicheng Li

    (University of Washington)

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).

Suggested Citation

  • Fang Han & Yicheng Li, 2020. "Moment Bounds for Large Autocovariance Matrices Under Dependence," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1445-1492, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00922-z
    DOI: 10.1007/s10959-019-00922-z
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    References listed on IDEAS

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    1. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    2. Fang Han & Han Liu, 2018. "ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 252-268, January.
    3. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2018. "Principal component analysis for second-order stationary vector time series," LSE Research Online Documents on Economics 84106, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Denis Chetverikov & Elena Manresa, 2022. "Spectral and post-spectral estimators for grouped panel data models," Papers 2212.13324, arXiv.org, revised Dec 2022.
    2. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.

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