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 such 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. (C) 2000 Elsevier Science Ltd. All rights reserved.