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textabstractSign-Perturbed Sums (SPS) is a finite sample system identification method that can build exact confidence regions for the unknown parameters of linear systems under mild statistical assumptions. Theoretical studies of the SPS method have assumed so far that the order of the system model is known to the user. In this paper we discuss the implications of this assumption for the applicability of the SPS method, and we propose an extension that, under mild assumptions, i) still delivers guaranteed confidence regions when the model order is correct, and ii) it is guaranteed to detect, in the long run, if the model order is wrong

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Undermodelling Detection with Sign-Perturbed Sums * *The work of A. Carè was supported by the European Re-search Consortium for Informatics and Mathematics (ERCIM) and the Australian Research Council (ARC) under Discovery Grant DP130104028. The work of M.C. Campi was partly supported by MIUR - Ministero dell’Istruzione, dell’Università e della Ricerca and by the H &amp; W program of the University of Brescia under the project CLAFITE. The work of B. Cs. Csáji was supported by the GINOP-2.3.2-15…