A finite-order stationary and minimum phase ARMA (p,q) model is equivalent to an infinite-order AR model. Two methods of estimating the parameters of the ARMA (p,q) model by solving only linear equations are based on or closely related to this equivalence relation. One method was derived directly from the equivalence relation by Graupe et al. The other was derived recently by Li and Dickinson based on an iterated LS regression approach. The end results bear close resemblance to those of Graupe et al. In this correspondence, the authors compare the two methods and suggest ways to improve the parameter estimates.