[Forum SIS] Seminar

[Simone Padoan]

Dear All,
We are glad to announce the following talk

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DEC - Statistics Seminar - Università Bocconi,

Monday, September 8th, 2014,

Room 3-E4-SR03, Via Roentgen 1 - 3rd floor

Time: 12:30pm

(The complete DEC seminars schedule is available at            
                 http://www.unibocconi.eu/statseminar)
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Speaker

Thomas Mikosch
(University of Copenhagen)

Title

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

Abstract

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 $\alpha\in (0,4)$; 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.

This is joint work with Richard A. Davis (Columbia NY) and
Oliver Pfaffel (Munich).



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Dr. Simone Padoan, PhD.
Assistant Professor

Department of Decision Sciences
Bocconi University of Milan
via Roentgen, 1 20136 Milano - Italy
tel. +39 02 5836 5368
Email: simone.padoan a unibocconi.it
Webpage: http://faculty.unibocconi.it/simonepadoan
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