  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.
