  The random matrix theory method of planar Gaussian diagrammatic expansion is
applied to find the mean spectral density of the Hermitian equal-time and
non-Hermitian time-lagged cross-covariance estimators, firstly in the form of
master equations for the most general multivariate Gaussian system, secondly
for seven particular toy models of the true covariance function. For the
simplest one of these models, the existing result is shown to be incorrect and
the right one is presented, moreover its generalizations are accomplished to
the exponentially-weighted moving average estimator as well as two non-Gaussian
distributions, Student t and free Levy. The paper revolves around applications
to financial complex systems, and the results constitute a sensitive probe of
the true correlations present there.
