On the use of the wavelet decomposition for time series prediction

This paper deals with nonlinear time series prediction. The proposed method combines the wavelet decomposition (as a filtering step) and neural networks to provide an acceptable prediction value. Basically, the wavelet decomposition uses a pair of filters to decompose iteratively the original time series. It results in a hierarchy of new time series that are easier to model and predict. These filters must satisfy some constraints such as causality, information lossless, etc. We prove here that our method reduces the empirical risk comparatively to the classical ones. As an illustration, the results obtained on both sunspot and MacKey–Glass time series are shown.