Dynamics of Quasi-Stationary Systems: Finance As an Example

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This combined method also allows to set up new criteria for merging clusters to simplify the complexity of the system. The low-dimensional approach allows to recover the high-dimensional fixed points of the system by means of an optimization procedure.