  A parameterization that is a modified version of a previous work is proposed
for the returns and correlation matrix of financial time series and its
properties are studied. This parameterization allows easy introduction of
non-stationarity and it shows several of the characteristics of the true,
observed realizations, such as fat tails, volatility clustering, and a spectrum
of eigenvalues of the correlation matrix that can be understood as an extension
of Random Matrix Theory results. The predicted behavior of this
parameterization for the eigenvalues is compared with the eigenvalues of
Brazilian assets and it is shown that those predictions fit the data better
than Random Matrix Theory.
