AR, ARMA, and AR-in-noise modeling by fitting windowed correlation data

A method for autoregressive (AR) modeling of stationary stochastic signals has been proposed based upon fitting the model auto-correlation function to the estimated (biased) autocorrelation in the least-squares sense over more than the minimum number of autocorrelation values (Ref. 7). In this paper, the method is extended to the case of autoregressive-moving-average (ARMA) models, including the special case of AR signals in white noise, and both AR and ARMA examples are presented. This method differs from the well known method of overdetermined normal equations in that fitting error, not equation error, is minimized. The bias in the estimated correlation values is also readily compensated without amplifying the higher (noisy) correlation lags. Iterative algorithms are derived to solve the resulting nonlinear equations.