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Pré-Publication, Document De Travail Année : 2019

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

Résumé

The asymptotic behaviour of the distribution of the singular values to the square 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 et versions

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

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Philippe Loubaton, Leonid Pastur, Daria Tieplova. On the behaviour of large empirical autocovariance matrices between the past and the future. 2019. ⟨hal-02370315v1⟩
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