Global convergence conditions in maximum likelihood estimation

Maximum likelihood estimation has been widely applied in system identification because of consistency, its asymptotic efficiency and sufficiency. However, gradient-based optimisation of the likelihood function might end up in local convergence. In this article we derive various new non-local-minimum conditions in both open and closed-loop system when the noise distribution is a Gaussian process. Here we consider different model structures, in particular ARARMAX, BJ and OE models