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

Allez, Romain; Rhodes, Rémi; Vargas, Vincent (2015), Convergence of the spectrum of empirical covariance matrices for independent MRW processes, ESAIM. Probability and Statistics, 19, p. 327-360. http://dx.doi.org/10.1051/ps/2014028

Type
Article accepté pour publication ou publié
Date
2015
Journal name
ESAIM. Probability and Statistics
Volume
19
Publisher
EDP sciences
Pages
327-360
Publication identifier
Metadata
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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
MRW processes; Marchenko Pastur type