Correlation Dimension and the Quality of Forecasts Given by a Neural Network
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.
KeywordsTime Series Mean Square Error Correlation Dimension Multilayer Perceptron Sigmoid Activation Function
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