Consistency analysis of subspace identi"cation 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 su$cient assumptions which however does not include important model structures such as, e.g. Box}Jenkins. Based on a simple least-squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions su$cient for consistency and which includes any model structure. ( 2000 Elsevier Science Ltd. All rights reserved.