ARMA parameter estimation based on sample covariances, for missing data

In this paper we consider the problem of spectral estimation through ARMA modeling of stationary time series witch missing observations. We consider estimators based on the sample covariances, and present an asymptotically optimal estimator among this group. The algorithm is based on a nonlinear least squares fit of the sample covariances computed from the data with missing observations to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are shown to be asymptotically optimal. The performance of the algorithm is illustrated by a numerical example.