Non-parametric data selection for neural learning in non-stationary time series

When a parametric model of a non-stationary time series is constructed based on data, as is the case for neural networks, it is very important to train the model with a set of data which contains the underlying structure to be discovered. The regions where only a noisy behavior is observed should be ignored. Information about the predictability can be used for example to select regions where a temporal structure is visible in order to select data for training a neural network for prediction. In this paper, we present a non-parametric cumulant based statistical approach for detecting linear and nonlinear statistical dependences in non-stationary time series. The statistical dependence is detected by measuring the predictability, which tests the null hypothesis of statistical independence, expressed in Fourier-space, by the surrogate method. Therefore, the predictability is defined as a higher-order cumulant based significance, discriminating between the original data and a set of scrambled surrogate data which correspond to the null hypothesis of a non-causal relationship between past and present. In this formulation nonlinear and non-Gaussian temporal dependences can be detected in time series. We apply the herein presented data selection method to the task of predicting the daily relative differences of the DAX given 12 inputs. These input variables describe a so called technical model using only historical DAX prices and the total volume of the transactions at the stack market. (C) 1997 Elsevier Science Ltd.