Time series prediction using a multiresolution dynamic predictor
Fuchiang Rich Tsui · 1996
There are great demands for long term prediction of time series in many practical applications. Classical linear predictors, such as the Wiener, least-mean-square, and recursive-least-square predictors, provide one-step short-term prediction only. Artificial neural networks, especially, the recurrent neural network whose output is fed back to the input layer can provide longer term multi-step predictions, however, a large network size is often needed and its training generally requires an excessively long history of input. To reduce the computational complexity in the recurrent neural network and to increase the long-term prediction accuracy, we have utilized the wavelet transform in a set of recurrent neural networks at several scales to construct a long-term nonlinear-predictor via the prediction of wavelet coefficients. An efficient training has been achieved by means of these wavelet coefficients. To extend its applicability to nonstationary processes via piecewise stationary prediction, the structure of our neural network predictor is designed to provide periodic switching in the feedback path so that the recurrent neural networks give predictions during the mode, while the feedforward structure undergoes an one-step retraining during the off mode. This is performed by windowing the data and taking its discrete wavelet transform based on which the connection weights are updated. In the next windowed interval, new prediction is performed by the updated network. Because of this adaptive behavior, we name our adaptive predictor a dynamic predictor. Both the semi-orthogonal and compactly supported biorthogonal wavelet transforms have been investigated for the multiresolution dynamic predictor. The semi-orthogonal wavelet transform defined in the Sobolev space (the function space of finite energy signals with bounded integral of the second order derivative) can be computed from coarse scale levels to fine scale levels, greatly reducing the computational burden during the long-term prediction process. The compactly supported biorthogonal wavelet transform has many desirable properties, and can be realized precisely using an efficient algorithm. This investigation has shown an important decorrelation property for the compactly supported biorthogonal wavelet transform. Based on this property, the neural network for long-term prediction may use a smaller number of weights and fewer training data, while achieving a better performance. In cases where the coarse scales are of the primary interest, the use of the semi-orthogonal wavelet transform requires fewer computational steps than other types of wavelet transforms. The least-mean-square and recursive-least-square predictors have been experimentally compared with the recurrent neural networks for prediction of intracranial pressure data acquired in a Neuro Intensive Care Unit. The results have shown that our recurrent neural network outperforms the other two predictors on the prediction of wavelet coefficients.