Recurrent and Feedforward Polynomial Modeling of Coupled Time Series

We present two methods for the prediction of coupled time series. The first one is based on modeling the series by a dynamic system with a polynomial format. This method can be formulated in terms of learning in a recurrent network, for which we give a computationally effective algorithm. The second method is a purely feedforward σ-π network procedure whose architecture derives from the recurrence relations for the derivatives of the trajectories of a Ricatti format dynamic system. It can also be used for the modeling of discrete series in terms of nonlinear mappings. Both methods have been tested successfully against chaotic series.