Predictor input selection for two stage identification in dynamic networks

Recently, the Two-Stage method has been proposed as a tool to obtain consistent estimates of modules embedded in dynamic networks [1], [2]. However, for this method the variables that are included in the predictor model are currently not considered as a user choice. In this paper it is shown that there is considerable freedom as to which variables can be included in the predictor model as inputs, and still obtain consistent estimates of the module of interest. Conditions that the choice of predictor inputs must satisfy are presented. The conditions could be used to find the smallest number of predictor inputs for instance. Algorithms are presented for checking the conditions and obtaining the estimates.