Abstract
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 which we refer to as amplitudes. We are interested in the case of non-stationarity covariances, which we model by stochastic covariances with a stationary distribution. We present a 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 large amounts of data are available. The ensemble that we find is characterized by an algebraic distribution which improves the understanding of large events.
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