This paper accurately quantifies the way in which
noise induced estimation errors are dependent on model structure,
underlying system frequency response, measurement noise and input
excitation. This exposes several new principles. In particular, it
is shown here that when employing Output--Error
model structures in a prediction-error framework, then the ensuing
estimate variability in the frequency domain depends on the
underlying system pole positions. As well, it is also established
that the variability is affected by the choice of model structure,
in that it is twice as much when system poles are estimated as when
they are a-priori known and fixed, even though the model order is
the same in both cases. These results are unexpected according to
pre-existing theory.