Non-asymptotic quality assessment of generalised FIR models with periodic inputs

This paper presents new results on quality assessment of models identified from a finite data sample. Suppose that we are given a finite sample of measurements coming from a plant and that we are asked to provide a model of the plant along with a certification of the model quality. The certification of the model quality is a measure of how far the identified model can be from the best model in the selected model class. At the present state of knowledge, this task is not trivial to accomplish, especially in the presence of unmodelled dynamics. In this paper we focus on least squares identification of generalised FIR models and provide new finite sample bounds for the corresponding estimation error. Our method is based on tests involving permuted data sets and bears a promise of applicability to more general settings than the one developed in this paper.