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

Romain Allez, Rémi Rhodes, Vincent Vargas
2015 E S A I M: Probability & Statistics  
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. MSC 2000 subject classifications: primary 60B20, 60G18; secondary 60G15, 91G99
doi:10.1051/ps/2014028 fatcat:ilucqplfhjdefhfejflojmwjuq