Convergence of the spectrum of empirical covariance matrices for independent MRW processes

Author: Allez Romain   Rhodes Rémi   Vargas Vincent  

Publisher: Edp Sciences

E-ISSN: 1262-3318|19|issue|327-360

ISSN: 1292-8100

Source: ESAIM: Probability and Statistics, Vol.19, Iss.issue, 2015-10, pp. : 327-360

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We study the asymptotic of the spectral distribution for large empirical covariance matrices composed of independent lognormal 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. We also illustrate our results by numerical simulations.