Adding data process feedback to the nonlinear autoregressive model

A nonlinear autoregressive model, the process feedback nonlinear autoregressive (PFNAR) model, in which the autoregressive coe0cients are a function of the combination of past data, is proposed. The autoregressive coe0cients of the PFNAR model consist of sequential autoregressive parts, and a data process feedback part that feeds back the in2uence from previous data points with “signi4cant delays”. Simulation data generated by the PFNAR model is introduced and compared with the ordinary autoregressive model and exponential autoregressive model. As a real example, the model is applied to ear pulse data for controlling respiration. Compared with some nonlinear models that do not address the process feedback part within autoregressive coe0cients, the prediction error demonstrates distinct improvement. Autoregressive coe0cients generally describe the transformed characteristics of the data, and the coe0cients of the PFNAR model describe the characteristics at sample time intervals. The instantaneous transfer characteristics of the data show the complexity of the nonlinear dynamics of respiration. The PFNAR model may reveal the nonlinear dynamic system for pseudo-periodic biomedical oscillation generated by complex physiological phenomena. Furthermore, the model may be applied to determine the mechanisms of phenomena fed back to the data processes within a certain system. ? 2002 Elsevier Science B.V. All rights reserved.