Nonlinear time series prediction based on a power-law noise model

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.