I'm struggling with Reinsel's book "Elements of Multivariate Time Series Analysis," because I thought that it would be a good idea to switch from Vector ARMA to state-space representations; particularly after reading What are disadvantages of state-space models and Kalman Filter for time-series modelling?, and after struggling with parameter estimation of VARMA processes.
The problem is that I can't see how correlation between two time series can be modeled in state-space representations. Is it that the correlation appears in the error covariance matrices? It sounds weird to me, particularly coming from VARMA. (Switching to state-space models is being harder than I thought!)