Lower bounds on the achievable estimation accuracy of stationary linear processes in the presence of energy-bounded exogenous signals are derived. These bounds are determined by the zeros of the process transfer function matrix. A significant difference is observed between the minimum-phase and the nonminimum-phase cases. In the latter case a lower bound is derived also for the norm of the matrix that solves the corresponding Riccati equation. The difference between the cases of minimum and nonminimum phase is accentuated when the measurement noise intensity tends to zero. It is shown that in the minimum-phase case the corresponding filter gain is almost in the range of the process input matrix. In the nonminimum-phase case the columns of the corresponding gain tend to stay in the space spanned by the rom of the system output matrix.