Matrix computations (3rd ed.)
Nonlinear time series analysis
Nonlinear time series analysis
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
International Journal of Systems Science
Predicting Chaotic Time Series Using Neural and Neurofuzzy Models: A Comparative Study
Neural Processing Letters
Neural Networks in Finance: Gaining Predictive Edge in the Market (Academic Press Advanced Finance Series)
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Fuzzy Sets and Systems
Time-series forecasting using flexible neural tree model
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A locally linear RBF network-based state-dependent AR model for nonlinear time series modeling
Information Sciences: an International Journal
A hybrid SARIMA wavelet transform method for sales forecasting
Decision Support Systems
Composite Function Wavelet Neural Networks with Differential Evolution and Extreme Learning Machine
Neural Processing Letters
Evolving Compact and Interpretable Takagi–Sugeno Fuzzy Models With a New Encoding Scheme
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Forecasting time series with genetic fuzzy predictor ensemble
IEEE Transactions on Fuzzy Systems
A fuzzy-logic-based approach to qualitative modeling
IEEE Transactions on Fuzzy Systems
Prediction of noisy chaotic time series using an optimal radial basis function neural network
IEEE Transactions on Neural Networks
A parameter optimization method for radial basis function type models
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations
IEEE Transactions on Neural Networks
Hybrid adaptive wavelet-neuro-fuzzy system for chaotic time series identification
Information Sciences: an International Journal
Generalized dynamical fuzzy model for identification and prediction
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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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.