Consistency analysis of subspace identification methods based on a linear regression approach

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does not include important model structures as e.g. Box-Jenkins. Based on a simple least squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure