On the behavior of large empirical autocovariance matrices between the past and the future

Abstract

The asymptotic behavior of the distribution of the squared singular values of the sample autocovariance matrix between the past and the future of a high-dimensional complex Gaussian uncorrelated sequence is studied. Using Gaussian tools, it is established that the distribution behaves as a deterministic probability measure whose support [Formula: see text] is characterized. It is also established that the squared singular values are almost surely located in a neighborhood of [Formula: see text].