Volume 19, 2015
|Page(s)||327 - 360|
|Published online||09 October 2015|
Convergence of the spectrum of empirical covariance matrices for independent MRW processes
Revised: 12 September 2014
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.
Mathematics Subject Classification: 60B20 / 60G18 / 60G15 / 91G99
Key words: Multifractals / Marchenko-Pastur theorem / random matrices / Gaussian multiplicative chaos
© EDP Sciences, SMAI 2015
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