Variance error quantifications that are exact for finite model order

This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding seminal work on this problem provides general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore 'exact' for arbitrarily small true model order and apply to the general cases of output-error and box-Jenkins model structures.