Topological Properties in Identification and Modeling Techniques

The paper deals with the problem of finding models and predictions within a large set of time series or random processes. Nothing is assumed about their mutual influence and dependence. The problem can not be tackled efficiently, starting from a classical system identification approach. Indeed, the general optimal solution would provide a large number of models, since it would consider every possible interdependence. Then a suboptimal approach will be developed. The proposed technique will present interesting modelling properties which can interpreted in terms of graph theory. The application of this procedure will also be exploited as a tool to provide a clusterization of time series. Finally, we will show that it turns out to be a dynamical generalization of other techniques described in literature.