  Complex systems are often non-stationary, typical indicators are continuously
changing statistical properties of time series. In particular, the correlations
between different time series fluctuate. Models that describe the multivariate
amplitude distributions of such systems are of considerable interest. Extending
previous work, we view a set of measured, non-stationary correlation matrices
as an ensemble for which we set up a random matrix model. We use this ensemble
to average the stationary multivariate amplitude distributions measured on
short time scales and thus obtain for large time scales multivariate amplitude
distributions which feature heavy tails. We explicitly work out four cases,
combining Gaussian and algebraic distributions. The results are either of
closed forms or single integrals. We thus provide, first, explicit multivariate
distributions for such non-stationary systems and, second, a tool that
quantitatively captures the degree of non-stationarity in the correlations.
