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Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series
Post-edited
Authors : Mikosch, Thomas (Author of the conference)
CIRM (Publisher )
60G55 - Point processes
62G32 - Statistics of extreme values; tail inference
CIRM (Publisher )
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 $\alpha \in \left ( 0,4 \right )$; 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).
MSC Codes : 60G55 - Point processes
62G32 - Statistics of extreme values; tail inference
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/07/14 Conference Date : 16/07/14 Subseries : Research talks arXiv category : Probability ; Statistics Theory Mathematical Area(s) : Probability & Statistics Format : QuickTime (.mov) Video Time : 00:55:53 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-07-16_Mikosch.mp4 
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Information on the Event
Event Title : Extreme value theory and laws of rare events / Théorie des valeurs extrêmes et lois des évènements raresEvent Organizers : Freitas, Ana Cristina ; Freitas, Jorge ; Todd, Michael J. ; Vaienti, Sandro Dates : 14/07/14 - 18/07/14 Event Year : 2014 Event URL : http://www.mcs.st-and.ac.uk/~miket/CIRM_...
Citation Data
DOI : 10.24350/CIRM.V.18538803Cite this video as: Mikosch, Thomas (2014). Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18538803 URI : http://dx.doi.org/10.24350/CIRM.V.18538803 |
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