Neural network method for determining embedding dimension of a time series

A method is described for determining the optimal short-term prediction time-delay embedding dimension for a scalar time series by training an artificial neural network on the data and then determining the sensitivity of the output of the network to each time lag averaged over the data set. As a byproduct, the method identifies any intermediate time lags that do not influence the dynamics, thus permitting a possible further reduction in the required embedding dimension. The method is tested on four sample data sets and compares favorably with more conventional methods including false nearest neighbors and the ‘plateau dimension’ determined by saturation of the estimated correlation dimension. The proposed method is especially advantageous when the data set is small or contaminated by noise. The trained network could be used for noise reduction, forecasting, and estimating the dynamical and geometrical properties of the system that produced the data, such as the Lyapunov exponent, entropy, and attractor dimension.