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 p olynomial format. This method can be formulated in terms of learning i n a recurrent network, for which we give a computationally effective a lgorithm. The second method is a purely feedforward sigma-pi network p rocedure 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.