  High-order ARX models can be used to approximate a quite general class of
linear systems in a parametric model structure, and well-established methods
can then be used to retrieve the true plant and noise models from the ARX
polynomials. However, this commonly used approach is only valid when the plant
is stable or if the unstable poles are shared with the true noise model. In
this contribution, we generalize this approach to allow the unstable poles not
to be shared, by introducing modifications to correctly retrieve the noise
model and noise variance.
