Noisy time series prediction using M-estimator based robust radial basis function neural networks with growing and pruning techniques

Noisy time series prediction is attractive and challenging since it is essential in many fields, such as forecasting, modeling, signal processing, economic and business planning. Radial basis function (RBF) neural network is considered as a good candidate for the prediction problems due to its rapid learning capacity and, therefore, has been applied successfully to nonlinear time series modeling and forecasts. However, the traditional RBF network encounters two primary problems. The first one is that the network performance is very likely to be affected by noise. The second problem is about the determination of the number of hidden nodes. In this paper, we present an M-estimator based robust radial basis function (RBF) learning algorithm with growing and pruning techniques. The Welsch M-estimator and median scale estimator are employed to get rid of the influence from the noise. The concept of neuron significance is adopted to implement the growing and pruning techniques of network nodes. The proposed method not only eliminates the influence of noise, but also dynamically adjusts the number of neurons to approach an appropriate size of the network. The results from the experiments show that the proposed method can produce a minimum prediction error compared with other methods. Furthermore, even adding 30% additive noise of the magnitude of the data, this proposed method still can do a good performance.