ARMA spectral estimation of time series with missing observations

The problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered. A new ARMA method is proposed for this problem, based on nonlinear optimization of a weighted squared error criterion. The method can handle either regularly or randomly missing observations. As a special case, the method can handle the problem of missing sample covariances. The computational complexity is modest compared to exact maximum likelihood estimation of the same parameters.