Structure detection of NARMAX models using bootstrap methods

Systems described by nonlinear difference equations, linear-in-the-parameters, which expand the current output in terms of present and past inputs and past outputs are considered NARMAX (Nonlinear AutoRegressive, Moving Average eXogenous) models. Many systems are described by NARMAX models using only a few terms. However, depending on the order of the system, the number of candidate terms can be very large. Selection of a subset of these candidate terms is necessary for an efficient system description. This remains an unresolved issue in system identification for over-parameterized models. A bootstrap based structure detection algorithm is proposed as a means of determining the structure of highly over-parameterized models. The performance of our bootstrap structure detection technique was evaluated by using it to estimate the structure of two NARMAX models, with colored input and white, zero-mean, output additive noise, and comparing the results to those of the t-test and stepwise regression. The proposed method is simple to use and is robust in the presence of noise