Nonlinear time series analysis by neural networks: a case study.

This paper presents a neural network approach to time-series analysis of a univariate nonlinear system. Feedforward networks are studied, and an appropriate network size is determined by different criteria computed on the basis of the performance of the models on the training and test sets. The analysis and conclusions drawn are supported by studies of the phase portraits of the models. By a proper choice of network size, the problems of over-parameterization are demonstrated to be avoided. The overfitting observed for larger networks is analyzed and the underlying reasons for their worse generalization capabilities are explained. Finally, some observations are made on the approximation provided by an oversized network with weights determined by an incomplete (interrupted) training and that of the optimal-sized network.