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Neural Computation

September 1993, Vol. 5, No. 5, Pages 795-811
(doi: 10.1162/neco.1993.5.5.795)
© 1993 Massachusetts Institute of Technology
Recurrent and Feedforward Polynomial Modeling of Coupled Time Series
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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.