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Limiting spectral distributions for a class of high-dimensional time series

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STSW02 - Statistics of geometric features and new data types

This talk discusses extensions to the time series case of the Marcenko-Pastur law on limiting spectral distributions (LSDs) for the eigenvalues of high-dimensional sample covariance matrices. The main result will be on establishing a non-linear integral equation characterizing the LSD in terms of its Stieltjes transform. Intuition will be presented for the simple case of a first-order moving average time series and evidence will be provided, indicating the applicability of the result to problems involving to the estimation of certain quadratic forms as they arise, for example, when dealing with the Markowitz portfolio problem. The talk is based on joint work with Haoyang Liu (Florida State) and Debashis Paul (UC Davis).

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

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