The Role of the Embedding Dimension and Time Delay in Time Series Forecasting

A Multi Layer Perceptron with a tapped line as input, is used to forecast the hyperchaotic Rössler system state variables starting from measurements of one observable. The impact of the frequency with which data should be sampled, and the number of data points which should be used in the input representation is analysed making reference to the values of the embedding parameters evaluated with different algorithms. In particular, the fourth state variable has been chosen as observable, for which the estimation of the embedding parameters does not supply an unique result. A comparison of the results obtained using different inputs highlights how the choice of the observable influences the forecasting of nonlinear dynamics.