Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos

Abstract

Functional networks are a recently introduced extension of neural networks which deal with general functional models instead of sigmoidal-like ones. In this paper we show that functional network architectures provide simple and efficient techniques to model nonlinear time series. To this aim, the neural functions are approximated by finite combinations of known functions from a given family (polynomials, Fourier expansions, etc.) and the associated coefficients are estimated from data. In this paper we present two architectures from the same functional networks family, introducing efficient learning algorithms leading to error functions with a single global minimum that need not to be learned by an iterative process. We demonstrate the effectiveness of these models by applying them to several examples, including data from the Hénon, Holmes, Lozi and Burgers maps. Finally, we show that these models can also be used to extract information masked in chaotic time series.