An amplitude-dependent autoregressive model based on a radial basis functions expansion

The author presents a new type of nonlinear signal model which constitutes a natural extension of the classical exponential autoregressive (EXPAR) model introduced by T. Ozaki (1978). The EXPAR model is known to have the ability to reproduce phenomena such as limit cycles and chaos. However, it has limitations that have limited its range of application. It is shown that a proper interpretation of the dependence of the EXPAR coefficients on the past values of the signal in terms of a limited radial basis function (RBF) expansion produces in a natural way a more general model free of the limitations of the EXPAR model. Results on real and simulated signals demonstrate the potential of the new model.<>