A method for parameter estimation in the NARMAX model with ARCH errors by RBF networks

A multilayer neural network is used in a number of applications such as the prediction problem of nonlinear time series. A radial basis functions (RBF) model, which can be viewed as a three-layer NN with a linear output mapping, is capable of modeling a wide class of nonlinear functions with arbitrary accuracy. We demonstrate that it is feasible to identify a NARMAX-like structure by RBF networks, and to use this architecture for predicting the nonlinear time series (NARX model) with ARCH (autoregressive conditional heteroskedastic) errors. The effectiveness of the proposed RBF networks system is evaluated using computer simulation