On Dynamic Network Modeling of Stationary Multivariate Processes

We study the modeling of a stationary multivariate stochastic process as the output of a dynamic network driven by white noise. When this noise corresponds to the innovation, i.e. the unpredictable part of the process, we show that the network satisfies certain stability conditions. Restricting the network model to having diagonal noise structure, we show that the innovation-driven representation is unique and internally stable. We provide a one-to-one correspondence between this representation and the spectral factor associated with the innovation model. For two-node networks, we show that a representation with diagonal noise model can be obtained from a generic one through an explicit map.