Non-Parametric Model Structure Identification and Parametric Efficiency in Nonlinear State Dependent Parameter Models

Abstract

Although neuro-fuzzy models provide a very useful general approach to the data-based modelling of nonlinear systems, their normal 'black box' nature is often a deterrent to their use in many of the natural sciences, where representation in terms of differential equations, or equivalent difference equations, is normally required and where the internal functioning and physical meaning of the model system is an important aspect of the modelling exercise. Moreover, identification of the model's internal structure can lead to considerable simplification of the model and the avoidance of over-parameterization, with important consequences as regards the statistical efficiency of the model parameter estimates. This paper introduces a non-parametric approach to model structure identification, based on recursive fixed interval smoothing, and shows how it can prove advantageous in the final parametric modelling of stochastic dynamic systems