On feedback free stochastic processes

We consider the problem of modeling the interaction between stochastic processes using only second-order statistics. We represent the variables as Hilbert space valued stochastic processes and use the technique of resolution spaces. Thus, we are able to build the causality requirement directly into the problem. Our approach is constructive and applies equally well to stationary and nonstationary processes. The condition of causality is very useful in determining the structure of the system generating the observed variables.