Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series | Vidéo | Carmin.tv

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

De Thomas Mikosch

Apparaît dans la collection : Extreme value theory and laws of rare events / Théorie des valeurs extrêmes et lois des évènements rares

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 $\alpha \in \left ( 0,4 \right )$; 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 denite 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. This is joint work with Richard A. Davis (Columbia NY) and Oliver Pfaffel (Munich).

Informations sur la vidéo

Date de captation 16/07/2014
Date de publication 28/07/2014
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18538803
Citer cette vidéo Mikosch, Thomas (16/07/2014). Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18538803
URL https://dx.doi.org/10.24350/CIRM.V.18538803

Domaine(s)

Bibliographie

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Davis, R. A., Pfaffel, O., Stelzer, R. Limit theory for the largest eigenvalues of sample covariance matrices with heavy-tails. Stochastic Processes and their Applications, Volume 124, (2014), no. 1, 18-50 - http://dx.doi.org/10.1016/j.spa.2013.07.005
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