Optimal ARMA parameter estimation based on the sample covariances for data with missing observations

The problem of spectral estimation through the autoregressive moving-average (ARMA) modeling of stationary processes with missing observations is considered. A class of estimators based on the sample covariances is presented, and an asymptotically optimal estimator in this class is proposed. The proposed algorithm is based on a nonlinear-least-squares fit of the sample covariances computed from the data to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are explored and used to show that it is asymptotically optimal, in the sense of achieving the smallest possible asymptotic variance. The performance of the algorithm is illustrated by some numerical examples