Time series prediction with wavelet neural networks

ANN are powerful approximants of nonlinear functions adequate for model-free estimation of systems. The main features of artificial neural networks: massive parallelism, distribution of computation among similar quite simple processing elements and-especially-the ability to learn from examples and to self-adapt are very well suited for the multiresolution approach intrinsic to wavelets. Both feedforward and dynamic recurrent ANN with internal delay lines (FIR) have been successfully used for the prediction of time series. Wavelets offer an adequate framework for the representation of "natural" a signals and images that are described by piecewise smooth functions, with rather sharp transitions between neighboring domains. This results in a local correlation structure of signal samples, which decays fast for farther apart ones. A similar structure exists in the frequency domain, corresponding to the band structure of the natural sources spectra. Wavelet representations are adequate building blocks for rather general functions of the mentioned type. Combining the advantages offered by neural network processing, on one hand, with wavelet representation, on the other, is an attractive idea. The paper presents some examples of wavelet neural networks applied to time series prediction.