Predicting time series using neural networks with wavelet-based denoising layers

To avoid the need to pre-process noisy data, two special denoising layers based on wavelet multiresolution analysis have been integrated into layered neural networks. A gradient-based learning algorithm has been developed that uses the same cost function to set both the neural network weights and the free parameters of the denoising layers. The denoising layers, when integrated into feedforward and recurrent neural networks, were validated on three time series prediction problems: the logistic map, a rubber hardness time series, and annual average sunspot numbers. Use of the denoising layers improved the prediction accuracy in both cases.