The concept of d-Separation is a key tool to analyze stochastic models defined by probability distributions of random variables that admit a factorization described by a Directed Acyclic Graph.
However, in the area of dynamical systems, and especially control theory, it is common to find network models involving stochastic processes that influence each other according to a directed network where feedback loops may be present as well.
In this article, we show that the concept of d-Separation can still be applied to infer properties of least square estimators defined on subsets of stochastic processes, at least if their mutual influences are described by linear operators.
Similar results have been obtained by [Koster 99] in the domain of Structural Equation Models for random variables.