Performance analysis of estimation algorithms of nonstationary ARMA processes

The correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive (AR), moving average (MA), and ARMA systems. By using estimation residuals in place of immeasurable noise terms in information vector or matrix, we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity, ergodicity, or existence of higher order moments. Furthermore, we derive the conditions for convergence of the parameter estimation. The simulation results validate the convergence theorems proposed.