Stochastic approximation algorithms for identifying ARMA processes

Following the convergence proofs for stochastic approximation identification of pure autoregressive (AR) processes with dependent observations, as derived by Saridis and Stein, it is shown that the convergence for mixed autoregressive-moving-average (ARMA) cases can also be proved when none of the AR or the MA parameters or of the covariances are assumed known. Consequently, a generalized stochastic approximations identification procedure for ARMA processes is derived, which is extendable to any linear Kalrman filter models.