Correlation dimension and the quality of forecasts given by a neural network

Abstract

The problem addressed in this paper is searching for a dependence between the correlation dimension of a time series and the mean square error (MSE) obtained when predicting the future time series values using a multilayer perceptron. The relation between the correlantion dimension and the ability of a neural network to adapt to sample data represented by in-sample mean square error is also studied. The dependence between correlation dimension and in-sample and out-of-sample MSE is found in many real-life as well as artificial time series. The results presented in the paper were obtained using various neural network sizes and various activation functions of the output layer neurons. © Springer-Verlag Berlin Heidelberg 2005.