Wavelet based smoothing in time series prediction with neural networks

To reduce the influence of noise in time series pre-diction, a neural network, the multilayered percep-tron, is combined with smoothing units based on the wavelet multiresolution analysis. Two approaches are compared: smoothing based on the statistical criterion and smoothing which uses the prediction error as the criterion. For the latter an algorithm for simultaneous setting of free parameters of the smoothing unit and the multilayered perceptron is derived. Prediction of noisy time series is shown to be better with the model based on the prediction error.