Identification of unstable systems using output error and Box-Jenkins model structures

It is well known that the output error and Box-Jenkins model structures cannot be used for prediction error identification of unstable systems. The reason for this is that the predictors in this case generically will be unstable. Typically, this problem is handled by projecting the parameter vector onto the region of stability, which gives erroneous results when the underlying system is unstable. The main contribution of this work is that we derive modified, but asymptotically equivalent, versions of these model structures that can also be applied in the case of unstable systems.