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Spectra of Sample Auto-Covariance Matrices

Date: 
Thursday 23rd April 2015 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
This work is based on R. Kühn and P. Sollich 2012 EPL 99 20008 doi:10.1209/0295-5075/99/20008

In this paper we compute spectra of sample auto-covariance matrices of stationary time series. The central result amounts to a generalization of Szeg"os theorem for spectra of Toeplitz matrices to the case with randomness due to finite sample effects. While the related problem of sample covariance matrices is well understood since the work of Marcenkov and Pastur, very little has been known about the sample auto-covariance problem.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons