A locally linear RBF network-based state-dependent AR model for nonlinear time series modeling

This paper presents a modeling approach to nonlinear time series that uses a set of locally linear radial basis function networks (LLRBFNs) to approximate the functional coefficients of the state-dependent autoregressive (SD-AR) model. The resulting model, called the locally linear radial basis function network-based autoregressive (LLRBF-AR) model, combines the advantages of the LLRBFN in function approximation and of the SD-AR model in nonlinear dynamics description. The LLRBFN weights that connect the hidden units with the output are linear functions of the input variables; this differs from the conventional RBF network weight structure. A structured nonlinear parameter optimization method (SNPOM) is applied to estimate the LLRBF-AR model parameters. Case studies on various time series and chaotic systems show that the LLRBF-AR modeling approach exhibits much better prediction accuracy compared to some other existing methods.