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Spectra of Sample Auto-Covariance Matrices

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Periodic and Ergodic Spectral Problems

This work is based on R. Khn 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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