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

Philippe Loubaton; Daria Tieplova

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arXiv · 1911.08933

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

Philippe Loubaton·Daria Tieplova

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Abstract

The asymptotic behaviour 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 the distribution behaves as a deterministic probability measure whose support S is characterized. It is also established that the singular values to the square are almost surely located in a neighbourhood of S.

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Philippe Loubaton, Daria Tieplova. 2019-11-20. On the behaviour of large empirical autocovariance matrices between the past and the future. https://arxiv.org/abs/1911.08933

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