Influence of data dimensionality on the quality of forecasts given by a multilayer perceptron

One of the phenomena that can be observed when using neural networks for time series prediction is that the quality of forecasts is correlated to the dimensionality of data. Higher data dimensionality leads in most cases to higher prediction errors. This phenomenon is connected by some authors to the decrease of the variance of the distance between data points which occurs when the length of predicted vectors increases. In this paper a proof is given that the variance of distance between data points also decreases with the correlation dimension of data. Therefore, the drop in forecast quality might be expected not only when the length of data vectors is increased but also when using vectors of the same length to represent data of increasing dimensionality. We also present some experimental results that illustrate the dependence between data dimensionality, variance of the distance between data points and the forecast error obtained when using a multilayer perceptron to predict future values of some time series.