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

Marwa Banna (1) , Florence Merlevède (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Sample covariance matrices; weak dependence; Lindeberg method; Marchenko-Pastur distributions; limiting spectral distribution

Domaines: Probabilités [math.PR]

Marwa Banna, Florence Merlevède. Limiting spectral distribution of large sample covariance matrices associated to a class of stationary processes. 2013. ⟨hal-00773140v2⟩