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Article overview
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Large sample autocovariance matrices of linear processes with heavy tails | | Johannes Heiny
; Thomas Mikosch
; | | Date: |
14 Jan 2020 | | Abstract: | We provide asymptotic theory for certain functions of the sample
autocovariance matrices of a high-dimensional time series with infinite fourth
moment. The time series exhibits linear dependence across the coordinates and
through time. Assuming that the dimension increases with the sample size, we
provide theory for the eigenvectors of the sample autocovariance matrices and
find explicit approximations of a simple structure, whose finite sample quality
is illustrated for simulated data. We also obtain the limits of the normalized
eigenvalues of functions of the sample autocovariance matrices in terms of
cluster Poisson point processes. In turn, we derive the distributional limits
of the largest eigenvalues and functionals acting on them. In our proofs, we
use large deviation techniques for heavy-tailed processes, point process
techniques motivated by extreme value theory, and related continuous mapping
arguments. | | Source: | arXiv, 2001.5056 | | Services: | Forum | Review | PDF | Favorites | |
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