Bootstrap Statistical Tests of Rank Determination for System Identification

Identification in the context of multivariate state space modelling involves the specification of the dimension of the state vector. One identification approach requires an estimate of the rank of a Hankel matrix. The most frequently used approaches of rank determination rely on information criteria methods. This paper evaluates the performance of some asymptotic tests of rank determination together with their bootstrapped versions against standard information criteria methods. This study is conducted through simulation experiments. Results show that the bootstrapped procedures significantly improve upon the performance of the corresponding asymptotic tests, and are proved better than standard Information Criterion methods.