Performance of parameter-magnitude based information criterion in identification of linear discrete-time model

Abstract

Information criterion is an important factor for model structure selection in system identification. It is used to determine the optimality of a particular model structure with the aim of selecting an adequate model. There had not been, or scarcely have been, any loss function that evaluates parsimony of model structures (bias contribution) based on the magnitude of parameter or coefficient. The magnitude of parameter could have a big role in choosing whether a term is significant enough to be included in a model and justifies ones' judgement in choosing or discarding a term/variable. This study intends to develop a new information criterion such that the bias contribution is related not only to the number of parameters, but mainly to the magnitude of the parameters. The parameter-magnitude based information criterion (PMIC2) is demonstrated in identification of linear discrete time model. The demonstration is tested using computational software on a number of simulated systems in the form of discrete-time linear regressive models of various lag orders and number of term/variables. It is shown that PMIC2 is able to select the correct the model based on all of the tested datasets.

Keywords: parameter magnitude, information criterion, system identification, discrete-time model, linear regressive model