Reasoning from non-stationarity

Complex real-world (biological) systems often exhibit intrinsically non-stationary behaviour of their temporal characteristics. We discuss local measures of scaling which can capture and reveal changes in a systemʹs behaviour. Such measures offer increased insight into a systemʹs behaviour and are superior to global, spectral characteristics like the multifractal spectrum. They are, however, often inadequate for fully understanding and modelling the phenomenon. We illustrate an attempt to capture complex 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 external descriptors/parameters, possibly influencing the systemʹs state, are used to span the search space investigated for the presence of a (sub-)optimal model. As an example, we use fetal heartbeat monitored during labour.