  The exact meaning of the noise spectrum of eigenvalues of the covariance
matrix is discussed. In order to better understand the possible phenomena
behind the observed noise, the spectrum of eigenvalues of the covariance matrix
is studied under a model where most of the true eigenvalues are zero and the
parameters are non-stationary. The results are compared with real observation
of Brazilian assets, suggesting that, although the non-stationarity seems to be
an important aspect of the problem, partially explaining some of the
eigenvalues as well as part of the kurtosis of the assets, it can not, by
itself, provide all the corrections needed to make the proposed model fit the
data perfectly.
