  In complex systems, crucial parameters are often subject to unpredictable
changes in time. Climate, biological evolution and networks provide numerous
examples for such non-stationarities. In many cases, improved statistical
models are urgently called for. In a general setting, we study systems of
correlated quantities to which we refer as amplitudes. We are interested in the
case of non-stationarity, i.e., seemingly random covariances. We present a
general method to derive the distribution of the covariances from the
distribution of the amplitudes. To ensure analytical tractability, we construct
a properly deformed Wishart ensemble of random matrices. We apply our method to
financial returns where the wealth of data allows us to carry out statistically
significant tests. The ensemble that we find is characterized by an algebraic
distribution which improves the understanding of large events.
