Adding data process feedback to the nonlinear autoregressive model

Hiroko Kato, Tohru Ozaki
2002 Signal Processing  
A nonlinear autoregressive model, the process feedback nonlinear autoregressive (PFNAR) model, in which the autoregressive coe cients are a function of the combination of past data, is proposed. The autoregressive coe cients of the PFNAR model consist of sequential autoregressive parts, and a data process feedback part that feeds back the in uence from previous data points with "signiÿcant delays". Simulation data generated by the PFNAR model is introduced and compared with the ordinary
more » ... essive 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 coe cients, the prediction error demonstrates distinct improvement. Autoregressive coe cients generally describe the transformed characteristics of the data, and the coe cients 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. ? conducted regarding nonlinear autoregressive models: bilinear autoregressive (AR) model [6], exponential AR (ExpAR) [7], threshold AR [18], nonlinear autoregressive moving average (ARMA) [3], autoregressive heteroscedastic (ARCH) [5] and extended approaches related to these models. The autoregressive coe cients are important for indicating the characteristics of the time series and this part of some nonlinear autoregressive models is often regarded as a function of the past data. Chen and Tsay [4] organized such models as a family in the functional-coe cient autoregressive (FCAR) model. 0165-1684/02/$ -see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 -1 6 8 4 ( 0 2 ) 0 0 1 3 9 -1
doi:10.1016/s0165-1684(02)00139-1 fatcat:kz6ghuifsvg2bf5ghs62s3th3i