Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series

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Standard

Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. / Davis, Richard A.; Mikosch, Thomas Valentin; Pfaffel, Olivier .

I: Stochastic Processes and Their Applications, Bind 126, Nr. 3, 2016, s. 767–799.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Davis, RA, Mikosch, TV & Pfaffel, O 2016, 'Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series', Stochastic Processes and Their Applications, bind 126, nr. 3, s. 767–799. https://doi.org/10.1016/j.spa.2015.10.001

APA

Davis, R. A., Mikosch, T. V., & Pfaffel, O. (2016). Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. Stochastic Processes and Their Applications, 126(3), 767–799. https://doi.org/10.1016/j.spa.2015.10.001

Vancouver

Davis RA, Mikosch TV, Pfaffel O. Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. Stochastic Processes and Their Applications. 2016;126(3):767–799. https://doi.org/10.1016/j.spa.2015.10.001

Author

Davis, Richard A. ; Mikosch, Thomas Valentin ; Pfaffel, Olivier . / Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. I: Stochastic Processes and Their Applications. 2016 ; Bind 126, Nr. 3. s. 767–799.

Bibtex

@article{c425f45c23c145ed849fbd64bbb23897,
title = "Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series",
abstract = "In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index α∈(0,4) in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative definite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum.",
author = "Davis, {Richard A.} and Mikosch, {Thomas Valentin} and Olivier Pfaffel",
year = "2016",
doi = "10.1016/j.spa.2015.10.001",
language = "English",
volume = "126",
pages = "767–799",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",
number = "3",

}

RIS

TY - JOUR

T1 - Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series

AU - Davis, Richard A.

AU - Mikosch, Thomas Valentin

AU - Pfaffel, Olivier

PY - 2016

Y1 - 2016

N2 - In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index α∈(0,4) in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative definite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum.

AB - In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index α∈(0,4) in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative definite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum.

U2 - 10.1016/j.spa.2015.10.001

DO - 10.1016/j.spa.2015.10.001

M3 - Journal article

VL - 126

SP - 767

EP - 799

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 3

ER -

ID: 154755231