ESTIMATION OF HIGHER-ORDER SPECTRA USING A NONLINEAR AUTOREGRESSIVE MODEL-BASED ON A LAYERED NEURAL-NETWORK

A method of determining the high-order spectral parameters of time ser ies by means of a nonlinear autoregressive model based on a layered ne ural network is described. In principle, describing the characteristic s of a time series consists of determining all of its finite-dimension al joint probability distribution functions. The output of a nonlinear system is usually a non-Gaussian time series. One way of describing s uch a series makes use of the higher-order spectra (cumulant spectra), including the power spectrum. In this paper we propose a method of ev aluating high-order spectra by means of an autoregressive model based on layered neural networks. After determining the weight parameters of the model by learning based on time series forecasting, we obtain the joint probability distributions by numerical methods, compute the hig her-order cumulant functions, and apply the multidimensional Fourier t ransform. We show that nonlinear autoregressive models based on layere d neural networks with a finite number of hidden units and with finite -valued weights always generate stationary time series. Numerical exam ples illustrating the possibility of obtaining smooth spectra are pres ented. (C) 1997 Scripta Technica, Inc.