Competitive chaotic AR(1) model estimation

Abstract

Chaotic signals, signals generated by a nonlinear dynamical system in chaotic state, may be useful models for many natural phenomena. In this paper we show a family of first-order difference equations with autocorrelation function identical to first-order autoregressive processes AR(1). We consider the maximum likelihood (ML) estimator of the model, and an efficient suboptimal method with reduced computational cost. However, for very large data records or on-line model estimation, even the suboptimal algorithm may have an excessive computational cost. In these cases we propose a low-cost competitive model estimation approach using an LMS-like algorithm for model training and adaption. Computer simulations show the good performance of this model estimation procedure.