In this paper, one aims at investigating the stability and convergence properties of a set membership identification methods involving ARMAX and OE model structures and optimal bounding ellipsoid based parameter adaptation. Fundamental results are obtained, they generalize some results that have been already established for FIR and ARX model structures.

In this paper we present a new model specification test for ARMAX models. The null hypothesis that the ARMAX model represents the conditional expectation of the dependent variable given the entire past of the economie time series process under review is tested against the alternative hypothesis that the null is false. The test involved is a consistent Standard nortnal test, as under the null hy...