Inferring causality in networks of WSS processes by pairwise estimation methods

Inferring causal dependences in a family of dynamic systems from a finite set of observations is a problem encountered in many applications that arise in a diverse variety of fields; ranging from economics and finance to climatology and neuroscience. Given a set of random processes, the objective is to determine whether one process is influenced by the others and to investigate the nature of this influence in case a dependence relation is identified. The notion of Granger-causality may be used in this context to measure and quantify causal structures. Ideally, in order to infer the complete interdependence structure of a complex system, one should simultaneously consider the dynamic behaviour of all the processes involved. However, for large networks, such a method becomes exceedingly complicated. In this paper, we consider an interdependent group of jointly wide sense stationary real-valued stochastic processes and investigate the problem of determining Granger-causality by identifying pairwise causal relations. It is seen that while such methods may not reveal all details of a system, they can nonetheless provide useful and reasonably accurate information.