A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry

A linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) ident ification algorithm is developed for modeling time series data. The new alg orithm is biased on the concepts of affine geometry in which the salient fe ature of the algorithm is to remove the linearly dependent ARMA vectors fro m the pool of candidate ARMA vectors. For noiseless time series data with a priori incorrect model-order selection, computer simulations show that acc urate linear and nonlinear ARMA model parameters can be obtained with the n ew algorithm. Many algorithms, including the fast orthogonal search (FOS) a lgorithm, are not able to obtain correct parameter estimates in every case, even with noiseless time series data, because their model-order search cri teria are suboptimal. For data contaminated with noise, computer simulation s show that the new algorithm performs better than the FOS algorithm for MA processes, and similarly to the FOS algorithm for ARMA processes. However, the computational time to obtain the parameter estimates with the new algo rithm is faster than with FOS. Application of the new algorithm to experime ntally obtained renal blood flow and pressure data show that the new algori thm is reliable in obtaining physiologically understandable transfer functi on relations between blood pressure and flow signals.