in this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.