Estimation for the autoregressive moving average process observed with noise

The autoregressive moving average process ARMA (p, q) observed with noise has another ARMA(p, k) representation, where k = max(p, q). Parameters for the ARMA(p,k) representation satisfy some non-linear restrictions. We develop restricted Newton-Raphson estimators of the ARMA(p, k) process which takes advantage of the information given in the non-linear restrictions. The asymptotic relative efficiency of the estimators indicates that the proposed restricted Newton-Raphson estimator is more efficient than the unrestricted Newton-Raphson estimator. In a Monte Carlo experiment, the proposed estimator is shown to perform better than the unrestricted estimator of the ARMA(p, k) process.