Non-stationarity in financial time series: Generic features and tail behavior

Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe limitations for approaches in the spirit of standard equilibrium statistical mechanics and thermodynamics. Nevertheless, we show that there are similar generic features which we uncover in the empirical multivariate return distributions for whole markets. We explain our findings by setting up a random matrix model