Large sample autocovariance matrices of linear processes with heavy tails

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Large sample autocovariance matrices of linear processes with heavy tails. / Heiny, Johannes; Mikosch, Thomas.

I: Stochastic Processes and Their Applications, Bind 141, 2021, s. 344-375.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Heiny, J & Mikosch, T 2021, 'Large sample autocovariance matrices of linear processes with heavy tails', Stochastic Processes and Their Applications, bind 141, s. 344-375. https://doi.org/10.1016/j.spa.2021.07.010

APA

Heiny, J., & Mikosch, T. (2021). Large sample autocovariance matrices of linear processes with heavy tails. Stochastic Processes and Their Applications, 141, 344-375. https://doi.org/10.1016/j.spa.2021.07.010

Vancouver

Heiny J, Mikosch T. Large sample autocovariance matrices of linear processes with heavy tails. Stochastic Processes and Their Applications. 2021;141:344-375. https://doi.org/10.1016/j.spa.2021.07.010

Author

Heiny, Johannes ; Mikosch, Thomas. / Large sample autocovariance matrices of linear processes with heavy tails. I: Stochastic Processes and Their Applications. 2021 ; Bind 141. s. 344-375.

Bibtex

@article{429ffb3a20324dde91984994a7a6d20f,
title = "Large sample autocovariance matrices of linear processes with heavy tails",
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.",
keywords = "Large deviations, Largest eigenvalues, Linearly dependent entries, Point process convergence, Regular variation, Sample autocovariance matrix",
author = "Johannes Heiny and Thomas Mikosch",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
doi = "10.1016/j.spa.2021.07.010",
language = "English",
volume = "141",
pages = "344--375",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",

}

RIS

TY - JOUR

T1 - Large sample autocovariance matrices of linear processes with heavy tails

AU - Heiny, Johannes

AU - Mikosch, Thomas

N1 - Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Large deviations

KW - Largest eigenvalues

KW - Linearly dependent entries

KW - Point process convergence

KW - Regular variation

KW - Sample autocovariance matrix

UR - http://www.scopus.com/inward/record.url?scp=85112526827&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2021.07.010

DO - 10.1016/j.spa.2021.07.010

M3 - Journal article

AN - SCOPUS:85112526827

VL - 141

SP - 344

EP - 375

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -

ID: 276652073