Parameter estimation for ARMA processes with errors in models

The data [bumpy equals]yn[bumpy equals] are fit by the ARMA process with possible model errors [bumpy equals][var epsilon]n[bumpy equals]:A(z) yn = C(z)wn + [var epsilon]n where [bumpy equals]wn, n[bumpy equals] is a martingale difference sequence. The recursive ELS algorithm is used to estimate unknown coefficients of A(z) and C(z). It is shown that the convergence rate of the estimate is and hence the estimate is strongly consistent if [summation operator]ni=0 ||[var epsilon]i||2 = o(n).