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Statistics Seminar 2019 - Eigenvalue distributions of sample (auto)covariance matrices obtained from high-dimensional linear processes

12/03/2019 dalle 16:30 alle 18:30

Dove Dipartimento di Scienze Statistiche - via delle Belle Arti 41 - Aula III - 2° piano

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Joint Statistics and Economics seminar

Relatore
Alexander Aue, University of California, Davis

Abstract
This talk is concerned with extensions of the classical Marcenko–Pastur law to time series. Specifically, p-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed entries possessing zero mean, unit variance and finite fourth moments. Under suitable assumptions on the coefficient matrices of the linear process, the limiting behavior of the empirical spectral distribution of both sample covariance and symmetrized sample autocovariance matrices is determined in the high-dimensional setting for which dimension p and sample size n diverge to infinity at the same rate. The results extend existing contributions available in the literature for the covariance case and are one of the first of their kind for the autocovariance case. The talk is based on joint work with Haoyang Liu (New York Fed) and Debashis Paul (UC Davis).

Organizzazione
Giuseppe Cavaliere e Alessandra Luati