Nonlinear time series modeling and prediction using functional weights wavelet neural network-based state-dependent AR model

摘要

This paper presents a Functional Weights Wavelet Neural Network-based state-dependent AR (FWWNN-AR) model with the main objective to address the modeling and prediction problem of nonlinear time series. The FWWNN-AR model is a state-dependent autoregressive (SD-AR) model, which has its coefficients approximated by a set of Functional Weights Wavelet Neural Network (FWWNN). The FWWNN is an enhanced type of wavelet neural network comprising of five layers: input, wavelet, product, output and functional weight layer that computes the weights as function of inputs thus making the weights to vary with the inputs and to share the dynamics with the wavelet compartment. The FWWNN-AR model possesses both the advantages of the state-dependent AR model in the description of nonlinear dynamics using few nodes and of the FWWNN in functional approximation considering mutually the time and frequency spaces. It learns the nonlinear dynamics from three distinct levels: AR level, Wavelet compartment level and functional weights level. A Structured Nonlinear Parameter Optimization Method (SNPOM) is applied to estimate the FWWNN-AR model parameters. This learning approach divides the parameter search space into linear and nonlinear subspaces and centers the search in the nonlinear subspace, but at each iteration in the optimization process, a search in the nonlinear (or linear) subspace is executed on the basis of the estimated values just obtained in linear (or nonlinear) subspace. The search in the nonlinear subspace uses a method similar to the Levemberg-Marquardt Method (LMM), and the search in the linear subspace uses the Least Square Method (LSM). The proposed model is validated by comparing its performances and effectiveness with those achieved by some well known models on both generated and real nonlinear time series.