Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure

Allez, Romain; Rhodes, Rémi; Vargas, Vincent

Allez, Romain; Rhodes, Rémi; Vargas, Vincent (2011), Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure. https://basepub.dauphine.fr/handle/123456789/17321

Type

Document de travail / Working paper

External document link

https://hal.archives-ouvertes.fr/hal-00604400

Date

2011

Series title

Cahier de recherche CEREMADE, Université Paris-Dauphine

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Author(s)

Allez, Romain

Rhodes, Rémi

Vargas, Vincent

Abstract (EN)

We study the asymptotics of the spectral distribution for large empirical covariance matrices composed of independent Multifractal Random Walk processes. The asymptotic is taken as the observation lag shrinks to $0$. In this setting, we show that there exists a limiting spectral distribution whose Stieltjes transform is uniquely characterized by equations which we specify.

Subjects / Keywords

Marchenko Pastur; random matrices; MRW; multifractal random walk; empirical covariance matrix; spectral measure