A learning algorithm for a hybrid nonlinear predictor applied to noisy nonlinear time series

A hybrid nonlinear time series predictor was proposed in which a nonlinear sub-predictor (NSP) and a linear sub-predictor (LSP) are combined in a cascade form. In this paper, we propose a separate learning method, in which the NSP is trained until convergence, then the LSP is trained using the final NSP weights. If the NSP and the LSP are trained simultaneously, the input of the LSP will be far from the correct prediction at the early iterations. This causes disturbance in the LSP learning process. The proposed separate learning method gives better results than the simultaneous one. Furthermore, a new learning algorithm for the NSP is proposed. By enforcing the NSP weights and biases to take large values until a certain number of the learning iterations, the input potential of the hidden neurons are expanded and shifted towards the saturation regions of the sigmoid functions. As a result, noise effects can be suppressed. Computer simulations, using real world time series, demonstrates usefulness of the proposals