The R and S arrays and the AIC in ARMA modeling and filter design

This paper compares an R and S array algorithm for estimation of an approximate AIC to exact maximum likelihood methods for autoregressive moving average (ARMA) model identification. In-earlierworks, the authors developed the R and S array methodology by first relating Levinson recursion to R and S array computations and then relating appropriate Yule-Walker quantities to the AIC. The resulting relationships provide an approximation of the product of innovation variance and the highest order moving average coefficient. Since this highest order coefficient becomes zero as model fit improves, estimation of this product is almost as desirable as more exact methods. Experiments indicate that for model determination, the numerical instability of the nonlinear methods employed to calculate the exact likelihood far outweighs its theoretically greater exactness.