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Journal Articles Random Matrices: Theory Appl. Year : 2021

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

Comportement asymptotique de grandes matrices d'autocovariance entre passé et futur

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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Dates and versions

hal-02370315 , version 1 (19-11-2019)
hal-02370315 , version 2 (25-11-2019)

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Philippe Loubaton, Daria Tieplova. On the behaviour of large empirical autocovariance matrices between the past and the future. Random Matrices: Theory Appl., 2021, vol. 10 (no. 2), ⟨10.1142/S2010326321500210⟩. ⟨hal-02370315v2⟩
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