Model selection for RBF network via generalized degree of freedom

Radial basis function (RBF) networks are considered in this study to simulate and forecast a chaotic time series. In order to evaluate the performance of the RBF networks, a new method is developed to calculate the generalized degree of freedom (GDF), which is used to obtain an unbiased estimation of variance of the fitted model error for the network. Numerical results show that the proposed estimation of GDF is more stable and faster than that obtained by the Monte Carlo method. A model selection method using GDF for a chaotic time series is then introduced and applied to four chaotic time series. The numerical results show that the network selected by the proposed method gives better prediction ability.