Reasoning from non-stationarity

Complex real-world (biological) systems often exhibit intrinsicallynon-stationary behaviour of their temporal characteristics.We discuss local measures of scaling which can capture andreveal changes in a system's behaviour. Such measures offer increasedinsight into a system's behaviour and are superior to global,spectral characteristics like the multifractal spectrum.They are, however, often inadequate for fully understanding andmodeling the phenomenon. We illustrate an attempt to capturecomplex model characteristics by analysing (multiple order)correlations in a high dimensional space of parameters of the(biological) system being studied. Both temporal information,among others local scaling information, and externaldescriptors/parameters, possibly influencing system's state, are usedto span the search space investigated for the presence of a (sub-)optimalmodel. As an example, we use fetal heartbeat monitored during labour.