Reconstruction of directed acyclic networks of dynamical systems

Determining the relation structure of various interconnected entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, detecting representative elements for an aggregate and determining reduced order models. Current methods tend to treat observations in a static manner by modeling the measured time series as repeated realizations of as many random variables that are independent over time. This amounts to assume static relationships among the measurements, making these techniques ill-suited for detecting propagative and dynamic phenomena that can be fundamental for the understanding of the system. In this paper we extend techniques for the identification of networks of random variables connected through static relations to the case of random processes with dynamic relations. This is achieved by showing that the Wiener filter defines a relationship among jointly stationary stochastic processes that has the properties of a semi-graphoid.