Adding data process feedback to the nonlinear autoregressive model

Abstract

A nonlinear autoregressive model, the process feedback nonlinear autoregressive (PFNAR) model, in which the autoregressive coefficients are a function of the combination of past data, is proposed. The autoregressive coefficients of the PFNAR model consist of sequential autoregressive parts, and a data process feedback part that feeds back the influence from previous data points with “significant 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 coefficients, the prediction error demonstrates distinct improvement. Autoregressive coefficients generally describe the transformed characteristics of the data, and the coefficients 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.