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Article Dans Une Revue Journal of Theoretical Probability Année : 2013

Limiting spectral distribution of large sample covariance matrices associated with a class of stationary processes

Résumé

In this paper we derive an extension of the Marchenko-Pastur theorem to a large class of weak dependent sequences of real random variables having only moment of order 2. Under mild dependence conditions that are easily verifiable in many situations, we derive that the limiting spectral distribution of the associated sample covariance matrix is characterised by an explicit equation for its Stieltjes transform, depending on the spectral density of the underlying process. Applications to linear processes, functions of linear processes and ARCH models are given.
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Dates et versions

hal-00773140 , version 1 (11-01-2013)
hal-00773140 , version 2 (16-01-2013)
hal-00773140 , version 3 (28-09-2013)

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Marwa Banna, Florence Merlevède. Limiting spectral distribution of large sample covariance matrices associated with a class of stationary processes. Journal of Theoretical Probability, 2013, pp.on line. ⟨10.1007/s10959-013-0508-x⟩. ⟨hal-00773140v3⟩
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